diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 790a344..fabcb79 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -53,13 +53,13 @@ jobs:
 
       - name: Test NetworkZ
         run: |
-          pytest --doctest-modules --durations=10
+          pytest
 
       - name: Test Dispatching
         # Limit this to only a single combination from the matrix
         if: ${{ (matrix.os == 'ubuntu') && (matrix.python-version == '3.11') }}
         run: |
-          NetworkZ_GRAPH_CONVERT=nx-loopback pytest --doctest-modules --durations=10
+          NetworkZ_GRAPH_CONVERT=nx-loopback pytest
 
   extra:
     runs-on: ${{ matrix.os }}
@@ -123,7 +123,7 @@ jobs:
 
       - name: Test NetworkZ
         run: |
-          pytest --doctest-modules --durations=10
+          pytest
 
   prerelease:
     runs-on: ${{ matrix.os }}-latest
@@ -147,4 +147,4 @@ jobs:
 
       - name: Test NetworkZ
         run: |
-          pytest --doctest-modules --durations=10
+          pytest
diff --git a/.gitignore b/.gitignore
index 93431b5..f944dfc 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,4 +1,5 @@
 scripts
+*.txt
 
 # Byte-compiled / optimized / DLL files
 __pycache__/
diff --git a/README.md b/README.md
index 5313b1e..f60430d 100644
--- a/README.md
+++ b/README.md
@@ -3,7 +3,10 @@
 NetworkZ is a library of graph algorithms in Python. It is an extension of the [NetworkX](https://github.com/networkx/networkx). It contains (by import) everything that is in NetworkX, plus some additional algorithms that were submitted into NetworkX but not merged yet. Currently, NetworkZ contains the following additional algorithms:
 
 * [Rank-maximal matching](networkz/algorithms/bipartite/rank_maximal_matching.py): by Oriya Alperin, Liel Vaknin and Amiel Lejzor.
+* [Maximum-weight fractional matching](networkz/algorithms/max_weight_fractional_matching.py): by Oriya Alperin, Liel Vaknin and Amiel Lejzor.
 * [Social-aware coalition formation](networkz/algorithms/approximation/coalition_formation.py) - by Victor Kushnir.
+* [Minimum cut on a graph with node capacity](networkz/algorithms/max_flow_with_node_capacity.py): by Yuval Bubnovsky, Almog David and Shaked Levi.
+* [Several approximate solutions to the Firefighter problem](networkz/algorithms/approximation/firefighter_problem): by Yuval Bubnovsky, Almog David and Shaked Levi.
 
 ## Installation
 
diff --git a/experiments/firefighter_problem/comparisons.py b/experiments/firefighter_problem/comparisons.py
new file mode 100644
index 0000000..75d6876
--- /dev/null
+++ b/experiments/firefighter_problem/comparisons.py
@@ -0,0 +1,407 @@
+"""
+
+The Paper - 
+Approximability of the Firefighter Problem Computing Cuts over Time
+
+Paper Link -
+https://www.math.uwaterloo.ca/~cswamy/papers/firefighter-journ.pdf
+
+Authors - 
+Elliot Anshelevich
+Deeparnab Chakrabarty
+Ameya Hate 
+Chaitanya Swamy
+
+Developers - 
+Yuval Bubnovsky
+Almog David
+Shaked Levi
+
+"""
+
+import experiments_csv
+from experiments_csv import *
+import logging
+from time import perf_counter
+import pandas as pd
+import random
+
+from networkz.algorithms.approximation.firefighter_problem.Utils import *
+from networkz.algorithms.approximation.firefighter_problem.Firefighter_Problem import *
+from networkz.algorithms.approximation.firefighter_problem.Random_Graph_Generator import generate_random_layered_network
+from networkz.algorithms.approximation.firefighter_problem.Random_Graph_Generator import generate_random_DiGraph
+
+logger = logging.getLogger(__name__)
+
+def setup_global_logger(level: int = logging.DEBUG):
+    """
+    Setup the global logger with a specific format and logging level.
+
+    Parameters:
+    ----------
+    level : int
+        Logging level, e.g., logging.DEBUG, logging.INFO.
+    """
+    log_format = "|| %(asctime)s || %(levelname)s || %(message)s"
+    date_format = '%H:%M:%S'
+    formatter = logging.Formatter(log_format, datefmt=date_format)
+    handler = logging.StreamHandler()
+    handler.setFormatter(formatter)
+    
+    root_logger = logging.getLogger()
+    root_logger.setLevel(level)
+    root_logger.addHandler(handler)
+
+def runner_no_spreading(algorithm, graph, source, targets):
+    """
+    Run the specified algorithm without spreading.
+
+    Parameters:
+    ----------
+    algorithm : function
+        The algorithm to be executed.
+    graph : nx.Graph
+        The graph on which the algorithm is to be run.
+    source : int
+        The source node.
+    targets : list
+        The target nodes to be saved.
+
+    Returns:
+    -------
+    dict:
+        A dictionary containing the budget used by the algorithm.
+    """
+    if algorithm == heuristic_minbudget:
+        result = algorithm(Graph=graph, source=source, targets=targets, spreading=False)
+        return {"Budget": result}
+    else:
+        result = algorithm(Graph=graph, source=source, targets=targets)
+        return {"Budget": result}
+
+def runner_spreading(algorithm, graph, budget, source, targets):
+    """
+    Run the specified algorithm with spreading.
+
+    Parameters:
+    ----------
+    algorithm : function
+        The algorithm to be executed.
+    graph : nx.Graph
+        The graph on which the algorithm is to be run.
+    source : int
+        The source node.
+    targets : list
+        The target nodes to be saved.
+
+    Returns:
+    -------
+    dict:
+        A dictionary containing the budget used or nodes saved by the algorithm.
+    """
+    if algorithm == heuristic_minbudget:
+        return {"Budget": (algorithm(Graph=graph, source=source, targets=targets, spreading=True))}
+    
+    if algorithm == heuristic_maxsave:
+        return {"Nodes_Saved": (str(len(algorithm(Graph=graph, budget=budget, source=source, targets=targets, spreading=True)[1])))}
+    
+    if algorithm == spreading_maxsave:
+        return {"Nodes_Saved": (str(len(algorithm(Graph=graph, budget=budget, source=source, targets=targets)[1])))}
+    
+    else:
+        return {"Budget": (algorithm(Graph=graph, source=source, targets=targets))}
+
+def Compare_NonSpread():
+    """
+    Compare the performance of different algorithms without spreading.
+
+    This function runs multiple experiments on randomly generated layered networks
+    and plots the results comparing the budget used by different algorithms.
+    """
+    ex1 = experiments_csv.Experiment("./experiments/", "non_spreading.csv", backup_folder=None)
+    ex1.clear_previous_results()  # to clear previous experiments
+
+    input_ranges = {
+        "algorithm": [non_spreading_dirlaynet_minbudget, non_spreading_minbudget, heuristic_minbudget],
+    }
+
+    def multiple_runs(runs=30):
+        for _ in range(runs):
+            graph = generate_random_layered_network() 
+            source = 0
+            nodes = list(graph.nodes)
+            nodes.remove(0)
+            num_targets = random.randint(1, int(len(nodes) / 4) + 1)
+            targets = random.sample(nodes, num_targets)
+            for algorithm in input_ranges["algorithm"]:
+                start_time = perf_counter()
+                result = runner_no_spreading(algorithm, graph, source, targets)
+                runtime = perf_counter() - start_time
+                ex1.add({**{"algorithm": algorithm.__name__, "runtime": runtime, "graph_nodes": len(graph.nodes)}, **result})
+        return {"status": "completed"}
+
+    # Set a time limit for the entire batch run
+    ex1.run_with_time_limit(multiple_runs, input_ranges={}, time_limit=0.9)
+
+    # Preprocess the DataFrame to extract numeric budget values
+    results_csv_file = "./experiments/non_spreading_minbudget.csv"
+    results = pd.read_csv(results_csv_file)
+
+    # Extract the numeric budget from the 'Budget' column
+    def extract_budget_numeric(budget):
+        if isinstance(budget, tuple):
+            return budget[0]
+        elif isinstance(budget, str):
+            try:
+                return eval(budget)[0]
+            except:
+                return None
+        return None
+
+    results['Budget_numeric'] = results['Budget'].apply(extract_budget_numeric)
+
+    # Drop rows where the 'Budget_numeric' is not available
+    results = results.dropna(subset=['Budget_numeric'])
+
+    # Save the preprocessed DataFrame to a temporary CSV file
+    preprocessed_csv_file = "./experiments/non_spreading_minbudget_preprocessed.csv"
+    results.to_csv(preprocessed_csv_file, index=False)
+
+    print("\n DataFrame-NonSpread: \n", results)
+
+    # Plot the results using the preprocessed CSV file
+    single_plot_results(
+        results_csv_file=preprocessed_csv_file,
+        filter={}, 
+        x_field="graph_nodes", 
+        y_field="Budget_numeric", 
+        z_field="algorithm", 
+        mean=True,
+        save_to_file="./experiments/non_spreading.png"
+    )
+    
+    print("\n DataFrame-NonSpread: \n", ex1.dataFrame)
+
+def Compare_SpreadingMaxSave():
+    """
+    Compare the performance of different algorithms with spreading for maximizing saved nodes.
+
+    This function runs multiple experiments on randomly generated directed graphs
+    and plots the results comparing the number of nodes saved by different algorithms.
+    """
+    ex2 = experiments_csv.Experiment("./experiments/", "spreading_maxsave.csv", backup_folder=None)
+    ex2.clear_previous_results()  # to clear previous experiments
+
+    input_ranges = {
+        "algorithm": [spreading_maxsave, heuristic_maxsave]
+    }
+    
+    node_counts = [100, 200, 400]
+    edge_probabilities = [0.1, 0.5, 0.8]
+    budget_range = [1,2,3,5,7,10]
+
+    def multiple_runs(runs=10):
+        for num_nodes in node_counts:
+            for edge_prob in edge_probabilities:
+                graph = generate_random_DiGraph(num_nodes=num_nodes, edge_probability=edge_prob, seed=None)
+                for _ in range(runs):
+                    source = 0
+                    nodes = list(graph.nodes)
+                    nodes.remove(0)
+                    num_targets = random.randint(1, int(len(nodes) / 2) + 1)
+                    targets = random.sample(nodes, num_targets)
+                    for budget in budget_range:
+                        for algorithm in input_ranges["algorithm"]:
+                            start_time = perf_counter()
+                            result = runner_spreading(algorithm, graph, budget, source, targets)
+                            runtime = perf_counter() - start_time
+                            
+                            ex2.add({**{"algorithm": algorithm.__name__, "runtime": runtime, "Budget": budget, "graph_nodes": num_nodes, "edge_probability": edge_prob}, **result})
+        return {"status": "completed"}
+
+    # Set a time limit for the entire batch run
+    ex2.run_with_time_limit(multiple_runs, input_ranges={}, time_limit=0.9)
+
+    ## DATA ISSUE WE HAD SO THIS IS A FIX ##
+    # Load the results
+    results_csv_file = "./experiments/spreading_maxsave.csv"
+    results = pd.read_csv(results_csv_file)
+
+    # Ensure 'algorithm' column is of type string
+    results['algorithm'] = results['algorithm'].astype(str)
+
+    # Ensure 'Budget' column is numeric and drop rows with NaNs
+    results['Budget'] = pd.to_numeric(results['Budget'], errors='coerce')
+    results = results.dropna(subset=['Budget'])
+
+    # Ensure 'Budget' is an integer
+    results['Budget'] = results['Budget'].astype(int)
+
+    # Ensure 'Nodes_Saved' column is numeric and drop rows with NaNs
+    results['Nodes_Saved'] = pd.to_numeric(results['Nodes_Saved'], errors='coerce')
+    results = results.dropna(subset=['Nodes_Saved'])
+
+    # Ensure 'Nodes_Saved' is an integer
+    results['Nodes_Saved'] = results['Nodes_Saved'].astype(int)
+
+    # Save the cleaned DataFrame to a new CSV file (optional, for debugging)
+    cleaned_csv_file = "./experiments/spreading_maxsave_preprocessed.csv"
+    results.to_csv(cleaned_csv_file, index=False)
+
+    # Plot the results using the cleaned DataFrame
+    multi_plot_results(
+        results_csv_file=cleaned_csv_file,
+        filter={}, 
+        subplot_rows=2,
+        subplot_cols=3,
+        x_field="graph_nodes", 
+        y_field="Nodes_Saved", 
+        z_field="algorithm", 
+        subplot_field="Budget",
+        sharex=True,
+        sharey=True,
+        mean=True,
+        save_to_file="./experiments/spreading_maxsave_budget.png"
+    )
+
+    multi_plot_results(
+        results_csv_file=cleaned_csv_file,
+        filter={"graph_nodes":100}, 
+        subplot_rows=3,
+        subplot_cols=1,
+        x_field="Budget", 
+        y_field="Nodes_Saved", 
+        z_field="algorithm", 
+        subplot_field="edge_probability",
+        sharex=True,
+        sharey=True,
+        mean=True,
+        save_to_file="./experiments/spreading_maxsave_100_edge_prob.png"
+    )
+
+    multi_plot_results(
+        results_csv_file=cleaned_csv_file,
+        filter={"graph_nodes":200}, 
+        subplot_rows=3,
+        subplot_cols=1,
+        x_field="Budget", 
+        y_field="Nodes_Saved", 
+        z_field="algorithm", 
+        subplot_field="edge_probability",
+        sharex=True,
+        sharey=True,
+        mean=True,
+        save_to_file="./experiments/spreading_maxsave_200_edge_prob.png"
+    )
+
+    multi_plot_results(
+        results_csv_file=cleaned_csv_file,
+        filter={"graph_nodes":400}, 
+        subplot_rows=3,
+        subplot_cols=1,
+        x_field="Budget", 
+        y_field="Nodes_Saved", 
+        z_field="algorithm", 
+        subplot_field="edge_probability",
+        sharex=True,
+        sharey=True,
+        mean=True,
+        save_to_file="./experiments/spreading_maxsave_400_edge_prob.png"
+    )
+
+    print("\n DataFrame-NonSpread: \n", ex2.dataFrame)
+
+def Compare_SpreadingMinBudget():
+    """
+    Compare the performance of different algorithms with spreading for minimizing the budget.
+
+    This function runs multiple experiments on randomly generated directed graphs
+    and plots the results comparing the budget used by different algorithms.
+    """
+    ex3 = experiments_csv.Experiment("./experiments/", "spreading_minbudget.csv", backup_folder=None)
+    ex3.clear_previous_results()  # to clear previous experiments
+
+    input_ranges = {
+        "algorithm": [spreading_minbudget, heuristic_minbudget]
+    }
+    
+    node_counts = [100, 200, 400]
+    edge_probabilities = [0.1, 0.5, 0.8]
+
+    def multiple_runs(runs=10):
+        for num_nodes in node_counts:
+            for edge_prob in edge_probabilities:
+                graph = generate_random_DiGraph(num_nodes=num_nodes, edge_probability=edge_prob, seed=None)
+                for _ in range(runs):
+                    source = 0
+                    nodes = list(graph.nodes)
+                    nodes.remove(0)
+                    num_targets = random.randint(1, int(len(nodes) / 2) + 1)
+                    targets = random.sample(nodes, num_targets)
+                    for algorithm in input_ranges["algorithm"]:
+                        start_time = perf_counter()
+                        result = runner_spreading(algorithm, graph, None, source, targets)
+                        runtime = perf_counter() - start_time
+                        ex3.add({**{"algorithm": algorithm.__name__, "runtime": runtime, "graph_nodes": num_nodes, "edge_probability": edge_prob}, **result})
+        return {"status": "completed"}
+
+    # Set a time limit for the entire batch run
+    ex3.run_with_time_limit(multiple_runs, input_ranges={}, time_limit=0.9)
+
+    # Preprocess the DataFrame to extract numeric budget values
+    results_csv_file = "./experiments/spreading_minbudget.csv"
+    results = pd.read_csv(results_csv_file)
+
+    # Extract the numeric budget from the 'Budget' column
+    def extract_budget_numeric(budget):
+        if isinstance(budget, tuple):
+            return budget[0]
+        elif isinstance(budget, str):
+            try:
+                return eval(budget)[0]
+            except:
+                return None
+        return None
+
+    results['Budget_numeric'] = results['Budget'].apply(extract_budget_numeric)
+
+    # Drop rows where the 'Budget_numeric' is not available
+    results = results.dropna(subset=['Budget_numeric'])
+
+    # Save the preprocessed DataFrame to a temporary CSV file
+    preprocessed_csv_file = "./experiments/spreading_minbudget_preprocessed.csv"
+    results.to_csv(preprocessed_csv_file, index=False)
+
+    print("\n DataFrame-NonSpread: \n", results)
+
+    # Plot the results using the preprocessed CSV file
+    single_plot_results(
+        results_csv_file=preprocessed_csv_file,
+        filter={}, 
+        x_field="graph_nodes", 
+        y_field="Budget_numeric", 
+        z_field="algorithm", 
+        mean=True,
+        save_to_file="./experiments/spreading_minbudget.png"
+    )
+
+    single_plot_results(
+        results_csv_file=preprocessed_csv_file,
+        filter={"edge_probability":0.1}, 
+        x_field="graph_nodes", 
+        y_field="Budget_numeric", 
+        z_field="algorithm", 
+        mean=True,
+        save_to_file="./experiments/spreading_minbudget_edge.png"
+    )
+    
+    print("\n DataFrame-NonSpread: \n", ex3.dataFrame)
+
+if __name__ == "__main__":
+    """To run this - please run one at a time; mark the others and then run"""
+
+    setup_global_logger(level=logging.DEBUG)
+
+    #Compare_NonSpread()
+    Compare_SpreadingMinBudget()
+    #Compare_SpreadingMaxSave()
\ No newline at end of file
diff --git a/experiments/firefighter_problem/non_spreading.csv b/experiments/firefighter_problem/non_spreading.csv
new file mode 100644
index 0000000..7c9b5f7
--- /dev/null
+++ b/experiments/firefighter_problem/non_spreading.csv
@@ -0,0 +1,92 @@
+algorithm,runtime,graph_nodes,Budget
+non_spreading_dirlaynet_minbudget,0.3383908999385312,140,"(4, {0: [2, 12, 97, 130], 2: [87, 110], 3: [97, 110], 4: [110], 5: [110]})"
+non_spreading_minbudget,0.015752499923110008,140,"(11, [])"
+heuristic_minbudget,0.798951999982819,140,"(4, [(2, 1), (12, 1), (10, 1), (6, 1), (34, 2), (30, 2), (33, 2), (37, 2), (48, 3), (47, 3), (42, 3), (40, 3), (60, 4), (53, 4), (59, 4), (67, 4), (87, 5), (69, 5), (75, 5), (77, 5), (97, 6), (99, 6), (95, 6), (98, 6), (102, 7), (110, 7), (107, 7), (105, 7)])"
+non_spreading_dirlaynet_minbudget,0.17233670002315193,110,"(9, {0: [7, 25, 17, 39, 31, 55, 66, 84, 91], 1: [39, 31, 55, 66, 91], 2: [55, 91], 4: [91], 5: [91]})"
+non_spreading_minbudget,0.01266180002130568,110,"(18, [])"
+heuristic_minbudget,0.7278256000718102,110,"(4, [(7, 1), (25, 1), (17, 1), (19, 1), (29, 2), (39, 2), (33, 2), (31, 2), (55, 3), (45, 3), (52, 3), (51, 3), (66, 4), (65, 4), (62, 4), (67, 4), (84, 5), (80, 5), (77, 5), (78, 5)])"
+non_spreading_dirlaynet_minbudget,0.36679140001069754,152,"(7, {0: [7, 14, 21, 78, 103, 109, 147], 1: [36], 4: [147]})"
+non_spreading_minbudget,0.020042599993757904,152,"(9, [])"
+heuristic_minbudget,1.0867155999876559,152,"(3, [(21, 1), (7, 1), (14, 1), (36, 2), (43, 2), (45, 2), (78, 3), (62, 3), (71, 3), (82, 4), (83, 4), (88, 4), (103, 5), (101, 5), (97, 5), (109, 6), (126, 6), (131, 6)])"
+non_spreading_dirlaynet_minbudget,0.5028269999893382,208,"(24, {0: [7, 14, 17, 23, 24, 9, 16, 1, 5, 22, 6, 15, 4, 13, 8, 18, 11, 21, 20, 10, 3, 12, 19, 2]})"
+non_spreading_minbudget,0.027307800017297268,208,"(24, [])"
+heuristic_minbudget,1.8271003999980167,208,"(9, [(23, 1), (22, 1), (20, 1), (18, 1), (17, 1), (3, 1), (9, 1), (8, 1), (4, 1), (53, 2), (32, 2), (37, 2), (27, 2), (48, 2), (31, 2), (40, 2), (46, 2), (39, 2), (77, 3), (69, 3), (64, 3), (67, 3), (66, 3), (56, 3), (79, 3), (72, 3), (61, 3), (85, 4), (86, 4), (82, 4), (91, 4), (84, 4), (87, 4), (88, 4), (90, 4), (93, 4), (106, 5), (109, 5), (99, 5), (95, 5), (98, 5), (96, 5), (108, 5), (103, 5), (97, 5), (126, 6), (114, 6), (117, 6), (113, 6), (111, 6), (130, 6), (119, 6), (118, 6), (121, 6), (136, 7), (135, 7), (146, 7), (150, 7), (158, 7), (139, 7), (154, 7), (144, 7), (145, 7), (167, 8), (169, 8), (163, 8), (166, 8), (165, 8), (162, 8), (168, 8), (164, 8)])"
+non_spreading_dirlaynet_minbudget,0.4180444999365136,180,"(11, {0: [5, 20, 13, 19, 2, 22, 58, 72, 118, 145, 168], 1: [22, 58, 72, 145, 168], 2: [58, 72, 118]})"
+non_spreading_minbudget,0.026318399934098125,180,"(19, [])"
+heuristic_minbudget,1.598106799996458,180,"(6, [(13, 1), (19, 1), (20, 1), (5, 1), (2, 1), (17, 1), (21, 2), (22, 2), (33, 2), (35, 2), (38, 2), (40, 2), (72, 3), (58, 3), (69, 3), (73, 3), (50, 3), (74, 3), (92, 4), (94, 4), (93, 4), (96, 4), (89, 4), (81, 4), (102, 5), (118, 5), (100, 5), (101, 5), (108, 5), (119, 5), (126, 6), (128, 6), (124, 6), (125, 6), (129, 6), (123, 6), (136, 7), (134, 7)])"
+non_spreading_dirlaynet_minbudget,0.2731701999437064,139,"(9, {0: [24, 25, 10, 5, 39, 38, 31, 40, 36], 1: [39, 38, 31, 40, 36, 45]})"
+non_spreading_minbudget,0.019093799986876547,139,"(15, [])"
+heuristic_minbudget,1.0293473000638187,139,"(6, [(25, 1), (24, 1), (10, 1), (5, 1), (8, 1), (20, 1), (34, 2), (36, 2), (38, 2), (39, 2), (33, 2), (30, 2), (46, 3), (42, 3), (44, 3), (45, 3), (55, 3), (43, 3), (63, 4), (72, 4), (69, 4), (62, 4), (65, 4), (64, 4), (83, 5), (92, 5), (91, 5), (77, 5), (90, 5), (82, 5), (97, 6), (99, 6), (101, 6), (98, 6), (100, 6), (104, 6), (107, 7), (109, 7), (110, 7)])"
+non_spreading_dirlaynet_minbudget,0.3905019999947399,184,"(12, {0: [25, 11, 20, 17, 37, 47, 79, 76, 97, 91, 96, 106], 1: [37, 47, 79, 76, 97, 91, 96, 106], 2: [79, 76, 97, 91, 96], 3: [97, 91, 96]})"
+non_spreading_minbudget,0.037450100062415004,184,"(24, [])"
+heuristic_minbudget,1.7678336999379098,184,"(6, [(17, 1), (25, 1), (11, 1), (20, 1), (2, 1), (13, 1), (43, 2), (47, 2), (37, 2), (50, 2), (33, 2), (57, 2), (82, 3), (77, 3), (79, 3), (76, 3), (59, 3), (70, 3), (88, 4), (92, 4), (97, 4), (87, 4), (94, 4), (86, 4), (111, 5), (113, 5), (109, 5), (114, 5), (125, 5), (122, 5), (140, 6), (138, 6), (135, 6), (141, 6), (129, 6), (127, 6), (151, 7), (152, 7), (144, 7), (150, 7), (162, 7), (142, 7)])"
+non_spreading_dirlaynet_minbudget,0.26434650004375726,116,"(9, {0: [4, 2, 8, 1, 5, 6, 3, 9, 32]})"
+non_spreading_minbudget,0.015567100024782121,116,"(9, [])"
+heuristic_minbudget,0.3790762999560684,116,"(6, [(2, 1), (1, 1), (9, 1), (4, 1), (5, 1), (8, 1), (14, 2), (39, 2), (13, 2), (24, 2), (31, 2), (19, 2), (44, 3), (61, 3), (55, 3), (42, 3), (60, 3), (48, 3), (69, 4), (76, 4), (72, 4), (62, 4), (73, 4), (64, 4)])"
+non_spreading_dirlaynet_minbudget,0.27031509997323155,146,"(3, {0: [23, 29, 97], 1: [105], 2: [55, 97], 3: [97], 4: [97]})"
+non_spreading_minbudget,0.01591560000088066,146,"(9, [])"
+heuristic_minbudget,0.8679373000049964,146,"(2, [(23, 1), (1, 1), (29, 2), (31, 2), (55, 3), (58, 3), (60, 4), (63, 4), (88, 5), (93, 5), (98, 6), (101, 6), (106, 7), (109, 7), (116, 8), (120, 8)])"
+non_spreading_dirlaynet_minbudget,0.18942820001393557,99,"(7, {0: [7, 13, 11, 17, 49, 68, 98], 1: [49, 68, 98], 2: [49, 68, 98]})"
+non_spreading_minbudget,0.012153099989518523,99,"(13, [])"
+heuristic_minbudget,0.6063708999427035,99,"(4, [(7, 1), (13, 1), (17, 1), (11, 1), (24, 2), (41, 2), (39, 2), (21, 2), (48, 3), (50, 3), (49, 3), (55, 3), (68, 4), (85, 4), (71, 4), (64, 4)])"
+non_spreading_dirlaynet_minbudget,0.12446479999925941,82,"(7, {0: [24, 1, 20, 3, 19, 53, 58], 1: [58], 2: [58], 3: [58]})"
+non_spreading_minbudget,0.007472099969163537,82,"(10, [])"
+heuristic_minbudget,0.5537956999614835,82,"(5, [(1, 1), (24, 1), (3, 1), (19, 1), (20, 1), (34, 2), (28, 2), (32, 2), (30, 2), (33, 2), (37, 3), (38, 3)])"
+non_spreading_dirlaynet_minbudget,0.17413019994273782,107,"(12, {0: [7, 4, 2, 8, 10, 11, 9, 1, 6, 3, 12, 5]})"
+non_spreading_minbudget,0.010613199905492365,107,"(12, [])"
+heuristic_minbudget,0.7465448000002652,107,"(8, [(6, 1), (12, 1), (1, 1), (11, 1), (3, 1), (7, 1), (10, 1), (5, 1), (23, 2), (16, 2), (28, 2), (15, 2), (18, 2), (26, 2), (22, 2), (24, 2), (41, 3), (36, 3), (38, 3), (49, 3), (46, 3), (32, 3), (47, 3), (44, 3), (63, 4), (54, 4), (58, 4), (64, 4), (62, 4), (53, 4), (61, 4), (60, 4), (69, 5), (75, 5), (67, 5), (79, 5), (80, 5), (78, 5), (74, 5), (82, 5), (84, 6), (85, 6), (86, 6), (87, 6)])"
+non_spreading_dirlaynet_minbudget,0.25344030000269413,134,"(20, {0: [7, 14, 17, 9, 16, 1, 5, 6, 15, 4, 8, 18, 11, 20, 10, 3, 12, 19, 2, 40]})"
+non_spreading_minbudget,0.08458460005931556,134,"(20, [])"
+heuristic_minbudget,0.6117942000273615,134,"(5, [(20, 1), (8, 1), (4, 1), (17, 1), (6, 1), (49, 2), (30, 2), (40, 2), (42, 2), (44, 2), (61, 3), (55, 3), (53, 3), (57, 3), (56, 3), (65, 4), (71, 4), (64, 4), (66, 4), (63, 4), (77, 5), (85, 5), (90, 5), (78, 5), (91, 5), (97, 6), (101, 6), (103, 6), (107, 6), (93, 6), (117, 7), (116, 7), (109, 7), (110, 7), (111, 7)])"
+non_spreading_dirlaynet_minbudget,0.17076830007135868,90,"(8, {0: [6, 1, 5, 30, 18, 43, 45, 64], 1: [30, 18, 43, 45, 64], 2: [43, 45, 64], 3: [64]})"
+non_spreading_minbudget,0.011342300102114677,90,"(14, [])"
+heuristic_minbudget,0.5426640999503434,90,"(4, [(6, 1), (1, 1), (5, 1), (4, 1), (30, 2), (18, 2), (29, 2), (37, 2), (52, 3), (45, 3), (43, 3), (48, 3), (73, 4), (64, 4), (66, 4), (80, 4)])"
+non_spreading_dirlaynet_minbudget,0.19489240006078035,112,"(9, {0: [7, 4, 2, 8, 1, 5, 6, 3, 9]})"
+non_spreading_minbudget,0.01148700003977865,112,"(9, [])"
+heuristic_minbudget,0.4493562000570819,112,"(4, [(9, 1), (5, 1), (3, 1), (6, 1), (24, 2), (19, 2), (10, 2), (13, 2), (28, 3), (37, 3), (41, 3), (26, 3), (58, 4), (66, 4), (47, 4), (60, 4), (74, 5), (79, 5), (76, 5), (83, 5), (89, 6), (88, 6), (85, 6), (87, 6), (91, 7), (92, 7), (95, 7), (98, 7)])"
+non_spreading_dirlaynet_minbudget,0.3376789001049474,148,"(11, {0: [7, 4, 8, 6, 11, 9, 1, 5, 10, 3, 2]})"
+non_spreading_minbudget,0.02147559996228665,148,"(11, [])"
+heuristic_minbudget,0.899608499952592,148,"(4, [(2, 1), (5, 1), (6, 1), (7, 1), (26, 2), (21, 2), (32, 2), (20, 2), (49, 3), (41, 3), (52, 3), (42, 3), (66, 4), (65, 4), (74, 4), (72, 4), (102, 5), (107, 5), (109, 5), (92, 5), (115, 6), (129, 6), (132, 6), (117, 6)])"
+non_spreading_dirlaynet_minbudget,0.16925049992278218,108,"(9, {0: [7, 4, 2, 8, 1, 5, 6, 3, 9]})"
+non_spreading_minbudget,0.010174600058235228,108,"(9, [])"
+heuristic_minbudget,0.37108299997635186,108,"(6, [(6, 1), (1, 1), (4, 1), (9, 1), (8, 1), (7, 1), (12, 2), (16, 2), (13, 2), (22, 2), (15, 2), (20, 2), (30, 3), (31, 3), (24, 3), (33, 3), (32, 3), (27, 3), (40, 4), (43, 4), (42, 4), (39, 4), (38, 4), (37, 4), (46, 5), (44, 5), (48, 5), (61, 5), (68, 5), (58, 5), (74, 6), (75, 6), (71, 6), (69, 6), (73, 6), (76, 6)])"
+non_spreading_dirlaynet_minbudget,0.17099270003382117,91,"(15, {0: [7, 4, 2, 13, 14, 8, 10, 11, 9, 6, 3, 12, 15, 5, 23]})"
+non_spreading_minbudget,0.010515599977225065,91,"(15, [])"
+heuristic_minbudget,0.5208220999920741,91,"(6, [(4, 1), (13, 1), (6, 1), (10, 1), (14, 1), (2, 1), (22, 2), (31, 2), (27, 2), (23, 2), (29, 2), (28, 2), (34, 3), (48, 3), (39, 3), (44, 3), (51, 3), (33, 3), (55, 4), (71, 4), (64, 4), (61, 4), (67, 4), (59, 4)])"
+non_spreading_dirlaynet_minbudget,0.15158629999496043,85,"(7, {0: [8, 20, 6, 27, 35, 46, 69], 1: [69]})"
+non_spreading_minbudget,0.008138900040648878,85,"(8, [])"
+heuristic_minbudget,0.3552039999049157,85,"(3, [(8, 1), (20, 1), (6, 1), (27, 2), (26, 2), (29, 2), (38, 3), (42, 3), (32, 3), (46, 4), (45, 4), (49, 4)])"
+non_spreading_dirlaynet_minbudget,0.22132230002898723,127,"(8, {0: [7, 4, 8, 1, 5, 6, 3, 2]})"
+non_spreading_minbudget,0.016545600024983287,127,"(8, [])"
+heuristic_minbudget,0.5257905001053587,127,"(6, [(6, 1), (1, 1), (5, 1), (2, 1), (4, 1), (7, 1), (28, 2), (11, 2), (27, 2), (14, 2), (29, 2), (12, 2), (41, 3), (43, 3), (46, 3), (48, 3), (42, 3), (40, 3), (67, 4), (71, 4), (56, 4), (49, 4), (62, 4), (69, 4), (73, 5), (75, 5), (91, 5), (83, 5), (81, 5), (80, 5), (98, 6), (101, 6), (94, 6), (99, 6), (92, 6), (95, 6)])"
+non_spreading_dirlaynet_minbudget,0.2360579000087455,129,"(7, {0: [7, 4, 1, 5, 6, 3, 2]})"
+non_spreading_minbudget,0.015887600020505488,129,"(7, [])"
+heuristic_minbudget,0.2970746000064537,129,"(3, [(5, 1), (2, 1), (7, 1), (16, 2), (8, 2), (13, 2), (27, 3), (24, 3), (22, 3), (28, 4), (29, 4), (32, 4), (43, 5), (45, 5), (38, 5), (52, 6), (53, 6), (56, 6), (64, 7), (62, 7), (69, 7), (83, 8), (93, 8), (98, 8)])"
+non_spreading_dirlaynet_minbudget,0.3081332999281585,149,"(22, {0: [7, 14, 17, 9, 16, 1, 5, 22, 6, 15, 4, 13, 8, 18, 11, 21, 20, 10, 3, 12, 19, 2]})"
+non_spreading_minbudget,0.020257299998775125,149,"(22, [])"
+heuristic_minbudget,0.8213011999614537,149,"(9, [(18, 1), (16, 1), (19, 1), (11, 1), (14, 1), (17, 1), (13, 1), (10, 1), (5, 1), (47, 2), (35, 2), (28, 2), (43, 2), (34, 2), (46, 2), (45, 2), (32, 2), (39, 2), (56, 3), (71, 3), (54, 3), (57, 3), (67, 3), (53, 3), (55, 3), (68, 3), (72, 3), (80, 4), (76, 4), (74, 4), (79, 4), (78, 4), (77, 4), (75, 4)])"
+non_spreading_dirlaynet_minbudget,0.21045160002540797,110,"(5, {0: [14, 43, 24, 45, 102], 1: [43, 24, 102]})"
+non_spreading_minbudget,0.012047900003381073,110,"(8, [])"
+heuristic_minbudget,0.7300266999518499,110,"(4, [(14, 1), (19, 1), (15, 1), (12, 1), (44, 2), (27, 2), (24, 2), (43, 2), (45, 3), (52, 3), (56, 3), (49, 3), (71, 4), (73, 4), (61, 4), (70, 4), (80, 5), (77, 5), (81, 5), (86, 5)])"
+non_spreading_dirlaynet_minbudget,0.27784580003935844,138,"(6, {0: [7, 15, 9, 39, 49, 51], 1: [39, 49, 51], 2: [49, 51]})"
+non_spreading_minbudget,0.020029000006616116,138,"(11, [])"
+heuristic_minbudget,0.8300812999950722,138,"(5, [(9, 1), (15, 1), (7, 1), (18, 1), (1, 1), (39, 2), (48, 2), (28, 2), (31, 2), (36, 2), (53, 3), (51, 3), (52, 3), (49, 3), (50, 3), (70, 4), (64, 4)])"
+non_spreading_dirlaynet_minbudget,0.31440829997882247,163,"(6, {0: [23, 20, 39, 43, 51, 50], 1: [39, 43, 51, 50], 2: [51, 50]})"
+non_spreading_minbudget,0.01737050001975149,163,"(10, [])"
+heuristic_minbudget,0.8383238000096753,163,"(4, [(23, 1), (20, 1), (7, 1), (22, 1), (39, 2), (26, 2), (43, 2), (27, 2), (51, 3), (52, 3), (50, 3), (53, 3), (67, 4), (78, 4), (77, 4), (69, 4), (87, 5), (93, 5), (80, 5), (97, 5), (122, 6), (115, 6), (116, 6), (121, 6), (125, 7), (123, 7), (126, 7), (127, 7)])"
+non_spreading_dirlaynet_minbudget,0.23480509989894927,93,"(10, {0: [7, 4, 8, 6, 11, 5, 10, 3, 2, 32]})"
+non_spreading_minbudget,0.009444999974220991,93,"(11, [])"
+heuristic_minbudget,0.25563530006911606,93,"(4, [(10, 1), (5, 1), (11, 1), (8, 1), (17, 2), (12, 2), (13, 2), (18, 2), (26, 3), (24, 3), (41, 3), (23, 3), (60, 4), (44, 4), (61, 4), (49, 4)])"
+non_spreading_dirlaynet_minbudget,0.47728039999492466,219,"(4, {0: [13, 19, 67, 173]})"
+non_spreading_minbudget,0.02702299994416535,219,"(5, [])"
+heuristic_minbudget,0.8602139001013711,219,"(2, [(19, 1), (13, 1), (43, 2), (46, 2), (58, 3), (56, 3), (62, 4), (67, 4), (97, 5), (74, 5), (101, 6), (108, 6), (126, 7), (140, 7)])"
+non_spreading_dirlaynet_minbudget,0.11988609994295985,73,"(1, {3: [67]})"
+non_spreading_minbudget,0.006057800026610494,73,"(2, [])"
+heuristic_minbudget,0.11525369994342327,73,"(1, [(3, 1), (9, 2), (34, 3), (46, 4)])"
+non_spreading_dirlaynet_minbudget,0.3718286999501288,178,"(5, {0: [4, 23, 59, 58, 70], 1: [59, 58], 2: [59, 58]})"
+non_spreading_minbudget,0.022550499998033047,178,"(9, [])"
+heuristic_minbudget,0.8823112000245601,178,"(3, [(4, 1), (23, 1), (8, 1), (52, 2), (53, 2), (29, 2), (59, 3), (54, 3), (60, 3), (61, 4), (68, 4), (70, 4), (76, 5), (77, 5), (78, 5), (102, 6), (99, 6), (97, 6), (118, 7), (127, 7), (113, 7), (142, 8), (150, 8), (155, 8)])"
+non_spreading_dirlaynet_minbudget,0.22105910000391304,119,"(2, {0: [42, 64], 1: [109], 2: [103], 3: [103]})"
+non_spreading_minbudget,0.013426600024104118,119,"(6, [])"
+heuristic_minbudget,0.5361911000218242,119,"(2, [(10, 1), (23, 1), (26, 2), (28, 2), (42, 3), (36, 3), (78, 4), (64, 4), (103, 5), (100, 5)])"
+,31.387649700045586,,
diff --git a/experiments/firefighter_problem/non_spreading_minbudget.png b/experiments/firefighter_problem/non_spreading_minbudget.png
new file mode 100644
index 0000000..8b74f04
Binary files /dev/null and b/experiments/firefighter_problem/non_spreading_minbudget.png differ
diff --git a/experiments/firefighter_problem/non_spreading_preprocessed.csv b/experiments/firefighter_problem/non_spreading_preprocessed.csv
new file mode 100644
index 0000000..2f04a8c
--- /dev/null
+++ b/experiments/firefighter_problem/non_spreading_preprocessed.csv
@@ -0,0 +1,91 @@
+algorithm,runtime,graph_nodes,Budget,Budget_numeric
+non_spreading_dirlaynet_minbudget,0.3383908999385312,140.0,"(4, {0: [2, 12, 97, 130], 2: [87, 110], 3: [97, 110], 4: [110], 5: [110]})",4.0
+non_spreading_minbudget,0.01575249992311,140.0,"(11, [])",11.0
+heuristic_minbudget,0.798951999982819,140.0,"(4, [(2, 1), (12, 1), (10, 1), (6, 1), (34, 2), (30, 2), (33, 2), (37, 2), (48, 3), (47, 3), (42, 3), (40, 3), (60, 4), (53, 4), (59, 4), (67, 4), (87, 5), (69, 5), (75, 5), (77, 5), (97, 6), (99, 6), (95, 6), (98, 6), (102, 7), (110, 7), (107, 7), (105, 7)])",4.0
+non_spreading_dirlaynet_minbudget,0.1723367000231519,110.0,"(9, {0: [7, 25, 17, 39, 31, 55, 66, 84, 91], 1: [39, 31, 55, 66, 91], 2: [55, 91], 4: [91], 5: [91]})",9.0
+non_spreading_minbudget,0.0126618000213056,110.0,"(18, [])",18.0
+heuristic_minbudget,0.7278256000718102,110.0,"(4, [(7, 1), (25, 1), (17, 1), (19, 1), (29, 2), (39, 2), (33, 2), (31, 2), (55, 3), (45, 3), (52, 3), (51, 3), (66, 4), (65, 4), (62, 4), (67, 4), (84, 5), (80, 5), (77, 5), (78, 5)])",4.0
+non_spreading_dirlaynet_minbudget,0.3667914000106975,152.0,"(7, {0: [7, 14, 21, 78, 103, 109, 147], 1: [36], 4: [147]})",7.0
+non_spreading_minbudget,0.0200425999937579,152.0,"(9, [])",9.0
+heuristic_minbudget,1.086715599987656,152.0,"(3, [(21, 1), (7, 1), (14, 1), (36, 2), (43, 2), (45, 2), (78, 3), (62, 3), (71, 3), (82, 4), (83, 4), (88, 4), (103, 5), (101, 5), (97, 5), (109, 6), (126, 6), (131, 6)])",3.0
+non_spreading_dirlaynet_minbudget,0.5028269999893382,208.0,"(24, {0: [7, 14, 17, 23, 24, 9, 16, 1, 5, 22, 6, 15, 4, 13, 8, 18, 11, 21, 20, 10, 3, 12, 19, 2]})",24.0
+non_spreading_minbudget,0.0273078000172972,208.0,"(24, [])",24.0
+heuristic_minbudget,1.8271003999980169,208.0,"(9, [(23, 1), (22, 1), (20, 1), (18, 1), (17, 1), (3, 1), (9, 1), (8, 1), (4, 1), (53, 2), (32, 2), (37, 2), (27, 2), (48, 2), (31, 2), (40, 2), (46, 2), (39, 2), (77, 3), (69, 3), (64, 3), (67, 3), (66, 3), (56, 3), (79, 3), (72, 3), (61, 3), (85, 4), (86, 4), (82, 4), (91, 4), (84, 4), (87, 4), (88, 4), (90, 4), (93, 4), (106, 5), (109, 5), (99, 5), (95, 5), (98, 5), (96, 5), (108, 5), (103, 5), (97, 5), (126, 6), (114, 6), (117, 6), (113, 6), (111, 6), (130, 6), (119, 6), (118, 6), (121, 6), (136, 7), (135, 7), (146, 7), (150, 7), (158, 7), (139, 7), (154, 7), (144, 7), (145, 7), (167, 8), (169, 8), (163, 8), (166, 8), (165, 8), (162, 8), (168, 8), (164, 8)])",9.0
+non_spreading_dirlaynet_minbudget,0.4180444999365136,180.0,"(11, {0: [5, 20, 13, 19, 2, 22, 58, 72, 118, 145, 168], 1: [22, 58, 72, 145, 168], 2: [58, 72, 118]})",11.0
+non_spreading_minbudget,0.0263183999340981,180.0,"(19, [])",19.0
+heuristic_minbudget,1.598106799996458,180.0,"(6, [(13, 1), (19, 1), (20, 1), (5, 1), (2, 1), (17, 1), (21, 2), (22, 2), (33, 2), (35, 2), (38, 2), (40, 2), (72, 3), (58, 3), (69, 3), (73, 3), (50, 3), (74, 3), (92, 4), (94, 4), (93, 4), (96, 4), (89, 4), (81, 4), (102, 5), (118, 5), (100, 5), (101, 5), (108, 5), (119, 5), (126, 6), (128, 6), (124, 6), (125, 6), (129, 6), (123, 6), (136, 7), (134, 7)])",6.0
+non_spreading_dirlaynet_minbudget,0.2731701999437064,139.0,"(9, {0: [24, 25, 10, 5, 39, 38, 31, 40, 36], 1: [39, 38, 31, 40, 36, 45]})",9.0
+non_spreading_minbudget,0.0190937999868765,139.0,"(15, [])",15.0
+heuristic_minbudget,1.0293473000638187,139.0,"(6, [(25, 1), (24, 1), (10, 1), (5, 1), (8, 1), (20, 1), (34, 2), (36, 2), (38, 2), (39, 2), (33, 2), (30, 2), (46, 3), (42, 3), (44, 3), (45, 3), (55, 3), (43, 3), (63, 4), (72, 4), (69, 4), (62, 4), (65, 4), (64, 4), (83, 5), (92, 5), (91, 5), (77, 5), (90, 5), (82, 5), (97, 6), (99, 6), (101, 6), (98, 6), (100, 6), (104, 6), (107, 7), (109, 7), (110, 7)])",6.0
+non_spreading_dirlaynet_minbudget,0.3905019999947399,184.0,"(12, {0: [25, 11, 20, 17, 37, 47, 79, 76, 97, 91, 96, 106], 1: [37, 47, 79, 76, 97, 91, 96, 106], 2: [79, 76, 97, 91, 96], 3: [97, 91, 96]})",12.0
+non_spreading_minbudget,0.037450100062415,184.0,"(24, [])",24.0
+heuristic_minbudget,1.7678336999379098,184.0,"(6, [(17, 1), (25, 1), (11, 1), (20, 1), (2, 1), (13, 1), (43, 2), (47, 2), (37, 2), (50, 2), (33, 2), (57, 2), (82, 3), (77, 3), (79, 3), (76, 3), (59, 3), (70, 3), (88, 4), (92, 4), (97, 4), (87, 4), (94, 4), (86, 4), (111, 5), (113, 5), (109, 5), (114, 5), (125, 5), (122, 5), (140, 6), (138, 6), (135, 6), (141, 6), (129, 6), (127, 6), (151, 7), (152, 7), (144, 7), (150, 7), (162, 7), (142, 7)])",6.0
+non_spreading_dirlaynet_minbudget,0.2643465000437572,116.0,"(9, {0: [4, 2, 8, 1, 5, 6, 3, 9, 32]})",9.0
+non_spreading_minbudget,0.0155671000247821,116.0,"(9, [])",9.0
+heuristic_minbudget,0.3790762999560684,116.0,"(6, [(2, 1), (1, 1), (9, 1), (4, 1), (5, 1), (8, 1), (14, 2), (39, 2), (13, 2), (24, 2), (31, 2), (19, 2), (44, 3), (61, 3), (55, 3), (42, 3), (60, 3), (48, 3), (69, 4), (76, 4), (72, 4), (62, 4), (73, 4), (64, 4)])",6.0
+non_spreading_dirlaynet_minbudget,0.2703150999732315,146.0,"(3, {0: [23, 29, 97], 1: [105], 2: [55, 97], 3: [97], 4: [97]})",3.0
+non_spreading_minbudget,0.0159156000008806,146.0,"(9, [])",9.0
+heuristic_minbudget,0.8679373000049964,146.0,"(2, [(23, 1), (1, 1), (29, 2), (31, 2), (55, 3), (58, 3), (60, 4), (63, 4), (88, 5), (93, 5), (98, 6), (101, 6), (106, 7), (109, 7), (116, 8), (120, 8)])",2.0
+non_spreading_dirlaynet_minbudget,0.1894282000139355,99.0,"(7, {0: [7, 13, 11, 17, 49, 68, 98], 1: [49, 68, 98], 2: [49, 68, 98]})",7.0
+non_spreading_minbudget,0.0121530999895185,99.0,"(13, [])",13.0
+heuristic_minbudget,0.6063708999427035,99.0,"(4, [(7, 1), (13, 1), (17, 1), (11, 1), (24, 2), (41, 2), (39, 2), (21, 2), (48, 3), (50, 3), (49, 3), (55, 3), (68, 4), (85, 4), (71, 4), (64, 4)])",4.0
+non_spreading_dirlaynet_minbudget,0.1244647999992594,82.0,"(7, {0: [24, 1, 20, 3, 19, 53, 58], 1: [58], 2: [58], 3: [58]})",7.0
+non_spreading_minbudget,0.0074720999691635,82.0,"(10, [])",10.0
+heuristic_minbudget,0.5537956999614835,82.0,"(5, [(1, 1), (24, 1), (3, 1), (19, 1), (20, 1), (34, 2), (28, 2), (32, 2), (30, 2), (33, 2), (37, 3), (38, 3)])",5.0
+non_spreading_dirlaynet_minbudget,0.1741301999427378,107.0,"(12, {0: [7, 4, 2, 8, 10, 11, 9, 1, 6, 3, 12, 5]})",12.0
+non_spreading_minbudget,0.0106131999054923,107.0,"(12, [])",12.0
+heuristic_minbudget,0.7465448000002652,107.0,"(8, [(6, 1), (12, 1), (1, 1), (11, 1), (3, 1), (7, 1), (10, 1), (5, 1), (23, 2), (16, 2), (28, 2), (15, 2), (18, 2), (26, 2), (22, 2), (24, 2), (41, 3), (36, 3), (38, 3), (49, 3), (46, 3), (32, 3), (47, 3), (44, 3), (63, 4), (54, 4), (58, 4), (64, 4), (62, 4), (53, 4), (61, 4), (60, 4), (69, 5), (75, 5), (67, 5), (79, 5), (80, 5), (78, 5), (74, 5), (82, 5), (84, 6), (85, 6), (86, 6), (87, 6)])",8.0
+non_spreading_dirlaynet_minbudget,0.2534403000026941,134.0,"(20, {0: [7, 14, 17, 9, 16, 1, 5, 6, 15, 4, 8, 18, 11, 20, 10, 3, 12, 19, 2, 40]})",20.0
+non_spreading_minbudget,0.0845846000593155,134.0,"(20, [])",20.0
+heuristic_minbudget,0.6117942000273615,134.0,"(5, [(20, 1), (8, 1), (4, 1), (17, 1), (6, 1), (49, 2), (30, 2), (40, 2), (42, 2), (44, 2), (61, 3), (55, 3), (53, 3), (57, 3), (56, 3), (65, 4), (71, 4), (64, 4), (66, 4), (63, 4), (77, 5), (85, 5), (90, 5), (78, 5), (91, 5), (97, 6), (101, 6), (103, 6), (107, 6), (93, 6), (117, 7), (116, 7), (109, 7), (110, 7), (111, 7)])",5.0
+non_spreading_dirlaynet_minbudget,0.1707683000713586,90.0,"(8, {0: [6, 1, 5, 30, 18, 43, 45, 64], 1: [30, 18, 43, 45, 64], 2: [43, 45, 64], 3: [64]})",8.0
+non_spreading_minbudget,0.0113423001021146,90.0,"(14, [])",14.0
+heuristic_minbudget,0.5426640999503434,90.0,"(4, [(6, 1), (1, 1), (5, 1), (4, 1), (30, 2), (18, 2), (29, 2), (37, 2), (52, 3), (45, 3), (43, 3), (48, 3), (73, 4), (64, 4), (66, 4), (80, 4)])",4.0
+non_spreading_dirlaynet_minbudget,0.1948924000607803,112.0,"(9, {0: [7, 4, 2, 8, 1, 5, 6, 3, 9]})",9.0
+non_spreading_minbudget,0.0114870000397786,112.0,"(9, [])",9.0
+heuristic_minbudget,0.4493562000570819,112.0,"(4, [(9, 1), (5, 1), (3, 1), (6, 1), (24, 2), (19, 2), (10, 2), (13, 2), (28, 3), (37, 3), (41, 3), (26, 3), (58, 4), (66, 4), (47, 4), (60, 4), (74, 5), (79, 5), (76, 5), (83, 5), (89, 6), (88, 6), (85, 6), (87, 6), (91, 7), (92, 7), (95, 7), (98, 7)])",4.0
+non_spreading_dirlaynet_minbudget,0.3376789001049474,148.0,"(11, {0: [7, 4, 8, 6, 11, 9, 1, 5, 10, 3, 2]})",11.0
+non_spreading_minbudget,0.0214755999622866,148.0,"(11, [])",11.0
+heuristic_minbudget,0.899608499952592,148.0,"(4, [(2, 1), (5, 1), (6, 1), (7, 1), (26, 2), (21, 2), (32, 2), (20, 2), (49, 3), (41, 3), (52, 3), (42, 3), (66, 4), (65, 4), (74, 4), (72, 4), (102, 5), (107, 5), (109, 5), (92, 5), (115, 6), (129, 6), (132, 6), (117, 6)])",4.0
+non_spreading_dirlaynet_minbudget,0.1692504999227821,108.0,"(9, {0: [7, 4, 2, 8, 1, 5, 6, 3, 9]})",9.0
+non_spreading_minbudget,0.0101746000582352,108.0,"(9, [])",9.0
+heuristic_minbudget,0.3710829999763518,108.0,"(6, [(6, 1), (1, 1), (4, 1), (9, 1), (8, 1), (7, 1), (12, 2), (16, 2), (13, 2), (22, 2), (15, 2), (20, 2), (30, 3), (31, 3), (24, 3), (33, 3), (32, 3), (27, 3), (40, 4), (43, 4), (42, 4), (39, 4), (38, 4), (37, 4), (46, 5), (44, 5), (48, 5), (61, 5), (68, 5), (58, 5), (74, 6), (75, 6), (71, 6), (69, 6), (73, 6), (76, 6)])",6.0
+non_spreading_dirlaynet_minbudget,0.1709927000338211,91.0,"(15, {0: [7, 4, 2, 13, 14, 8, 10, 11, 9, 6, 3, 12, 15, 5, 23]})",15.0
+non_spreading_minbudget,0.010515599977225,91.0,"(15, [])",15.0
+heuristic_minbudget,0.5208220999920741,91.0,"(6, [(4, 1), (13, 1), (6, 1), (10, 1), (14, 1), (2, 1), (22, 2), (31, 2), (27, 2), (23, 2), (29, 2), (28, 2), (34, 3), (48, 3), (39, 3), (44, 3), (51, 3), (33, 3), (55, 4), (71, 4), (64, 4), (61, 4), (67, 4), (59, 4)])",6.0
+non_spreading_dirlaynet_minbudget,0.1515862999949604,85.0,"(7, {0: [8, 20, 6, 27, 35, 46, 69], 1: [69]})",7.0
+non_spreading_minbudget,0.0081389000406488,85.0,"(8, [])",8.0
+heuristic_minbudget,0.3552039999049157,85.0,"(3, [(8, 1), (20, 1), (6, 1), (27, 2), (26, 2), (29, 2), (38, 3), (42, 3), (32, 3), (46, 4), (45, 4), (49, 4)])",3.0
+non_spreading_dirlaynet_minbudget,0.2213223000289872,127.0,"(8, {0: [7, 4, 8, 1, 5, 6, 3, 2]})",8.0
+non_spreading_minbudget,0.0165456000249832,127.0,"(8, [])",8.0
+heuristic_minbudget,0.5257905001053587,127.0,"(6, [(6, 1), (1, 1), (5, 1), (2, 1), (4, 1), (7, 1), (28, 2), (11, 2), (27, 2), (14, 2), (29, 2), (12, 2), (41, 3), (43, 3), (46, 3), (48, 3), (42, 3), (40, 3), (67, 4), (71, 4), (56, 4), (49, 4), (62, 4), (69, 4), (73, 5), (75, 5), (91, 5), (83, 5), (81, 5), (80, 5), (98, 6), (101, 6), (94, 6), (99, 6), (92, 6), (95, 6)])",6.0
+non_spreading_dirlaynet_minbudget,0.2360579000087455,129.0,"(7, {0: [7, 4, 1, 5, 6, 3, 2]})",7.0
+non_spreading_minbudget,0.0158876000205054,129.0,"(7, [])",7.0
+heuristic_minbudget,0.2970746000064537,129.0,"(3, [(5, 1), (2, 1), (7, 1), (16, 2), (8, 2), (13, 2), (27, 3), (24, 3), (22, 3), (28, 4), (29, 4), (32, 4), (43, 5), (45, 5), (38, 5), (52, 6), (53, 6), (56, 6), (64, 7), (62, 7), (69, 7), (83, 8), (93, 8), (98, 8)])",3.0
+non_spreading_dirlaynet_minbudget,0.3081332999281585,149.0,"(22, {0: [7, 14, 17, 9, 16, 1, 5, 22, 6, 15, 4, 13, 8, 18, 11, 21, 20, 10, 3, 12, 19, 2]})",22.0
+non_spreading_minbudget,0.0202572999987751,149.0,"(22, [])",22.0
+heuristic_minbudget,0.8213011999614537,149.0,"(9, [(18, 1), (16, 1), (19, 1), (11, 1), (14, 1), (17, 1), (13, 1), (10, 1), (5, 1), (47, 2), (35, 2), (28, 2), (43, 2), (34, 2), (46, 2), (45, 2), (32, 2), (39, 2), (56, 3), (71, 3), (54, 3), (57, 3), (67, 3), (53, 3), (55, 3), (68, 3), (72, 3), (80, 4), (76, 4), (74, 4), (79, 4), (78, 4), (77, 4), (75, 4)])",9.0
+non_spreading_dirlaynet_minbudget,0.2104516000254079,110.0,"(5, {0: [14, 43, 24, 45, 102], 1: [43, 24, 102]})",5.0
+non_spreading_minbudget,0.012047900003381,110.0,"(8, [])",8.0
+heuristic_minbudget,0.7300266999518499,110.0,"(4, [(14, 1), (19, 1), (15, 1), (12, 1), (44, 2), (27, 2), (24, 2), (43, 2), (45, 3), (52, 3), (56, 3), (49, 3), (71, 4), (73, 4), (61, 4), (70, 4), (80, 5), (77, 5), (81, 5), (86, 5)])",4.0
+non_spreading_dirlaynet_minbudget,0.2778458000393584,138.0,"(6, {0: [7, 15, 9, 39, 49, 51], 1: [39, 49, 51], 2: [49, 51]})",6.0
+non_spreading_minbudget,0.0200290000066161,138.0,"(11, [])",11.0
+heuristic_minbudget,0.8300812999950722,138.0,"(5, [(9, 1), (15, 1), (7, 1), (18, 1), (1, 1), (39, 2), (48, 2), (28, 2), (31, 2), (36, 2), (53, 3), (51, 3), (52, 3), (49, 3), (50, 3), (70, 4), (64, 4)])",5.0
+non_spreading_dirlaynet_minbudget,0.3144082999788224,163.0,"(6, {0: [23, 20, 39, 43, 51, 50], 1: [39, 43, 51, 50], 2: [51, 50]})",6.0
+non_spreading_minbudget,0.0173705000197514,163.0,"(10, [])",10.0
+heuristic_minbudget,0.8383238000096753,163.0,"(4, [(23, 1), (20, 1), (7, 1), (22, 1), (39, 2), (26, 2), (43, 2), (27, 2), (51, 3), (52, 3), (50, 3), (53, 3), (67, 4), (78, 4), (77, 4), (69, 4), (87, 5), (93, 5), (80, 5), (97, 5), (122, 6), (115, 6), (116, 6), (121, 6), (125, 7), (123, 7), (126, 7), (127, 7)])",4.0
+non_spreading_dirlaynet_minbudget,0.2348050998989492,93.0,"(10, {0: [7, 4, 8, 6, 11, 5, 10, 3, 2, 32]})",10.0
+non_spreading_minbudget,0.0094449999742209,93.0,"(11, [])",11.0
+heuristic_minbudget,0.255635300069116,93.0,"(4, [(10, 1), (5, 1), (11, 1), (8, 1), (17, 2), (12, 2), (13, 2), (18, 2), (26, 3), (24, 3), (41, 3), (23, 3), (60, 4), (44, 4), (61, 4), (49, 4)])",4.0
+non_spreading_dirlaynet_minbudget,0.4772803999949246,219.0,"(4, {0: [13, 19, 67, 173]})",4.0
+non_spreading_minbudget,0.0270229999441653,219.0,"(5, [])",5.0
+heuristic_minbudget,0.8602139001013711,219.0,"(2, [(19, 1), (13, 1), (43, 2), (46, 2), (58, 3), (56, 3), (62, 4), (67, 4), (97, 5), (74, 5), (101, 6), (108, 6), (126, 7), (140, 7)])",2.0
+non_spreading_dirlaynet_minbudget,0.1198860999429598,73.0,"(1, {3: [67]})",1.0
+non_spreading_minbudget,0.0060578000266104,73.0,"(2, [])",2.0
+heuristic_minbudget,0.1152536999434232,73.0,"(1, [(3, 1), (9, 2), (34, 3), (46, 4)])",1.0
+non_spreading_dirlaynet_minbudget,0.3718286999501288,178.0,"(5, {0: [4, 23, 59, 58, 70], 1: [59, 58], 2: [59, 58]})",5.0
+non_spreading_minbudget,0.022550499998033,178.0,"(9, [])",9.0
+heuristic_minbudget,0.8823112000245601,178.0,"(3, [(4, 1), (23, 1), (8, 1), (52, 2), (53, 2), (29, 2), (59, 3), (54, 3), (60, 3), (61, 4), (68, 4), (70, 4), (76, 5), (77, 5), (78, 5), (102, 6), (99, 6), (97, 6), (118, 7), (127, 7), (113, 7), (142, 8), (150, 8), (155, 8)])",3.0
+non_spreading_dirlaynet_minbudget,0.221059100003913,119.0,"(2, {0: [42, 64], 1: [109], 2: [103], 3: [103]})",2.0
+non_spreading_minbudget,0.0134266000241041,119.0,"(6, [])",6.0
+heuristic_minbudget,0.5361911000218242,119.0,"(2, [(10, 1), (23, 1), (26, 2), (28, 2), (42, 3), (36, 3), (78, 4), (64, 4), (103, 5), (100, 5)])",2.0
diff --git a/experiments/firefighter_problem/spreading_maxsave.csv b/experiments/firefighter_problem/spreading_maxsave.csv
new file mode 100644
index 0000000..402ba53
--- /dev/null
+++ b/experiments/firefighter_problem/spreading_maxsave.csv
@@ -0,0 +1,1082 @@
+algorithm,runtime,Budget,graph_nodes,edge_probability,Nodes_Saved
+spreading_maxsave,0.08716789999743924,1,100,0.1,17
+heuristic_maxsave,0.032615200034342706,1,100,0.1,17
+spreading_maxsave,0.08247730002040043,2,100,0.1,24
+heuristic_maxsave,0.03249310003593564,2,100,0.1,25
+spreading_maxsave,0.26054399996064603,3,100,0.1,31
+heuristic_maxsave,0.03926589997718111,3,100,0.1,31
+spreading_maxsave,0.13694779999786988,5,100,0.1,42
+heuristic_maxsave,0.11109409999335185,5,100,0.1,40
+spreading_maxsave,0.16288850002456456,7,100,0.1,44
+heuristic_maxsave,0.05416710005374625,7,100,0.1,46
+spreading_maxsave,0.20015620003687218,10,100,0.1,47
+heuristic_maxsave,0.04395620001014322,10,100,0.1,48
+spreading_maxsave,0.05649819999234751,1,100,0.1,5
+heuristic_maxsave,0.029464400024153292,1,100,0.1,5
+spreading_maxsave,0.07986429997254163,2,100,0.1,5
+heuristic_maxsave,0.03359050001017749,2,100,0.1,5
+spreading_maxsave,0.098236599995289,3,100,0.1,5
+heuristic_maxsave,0.08675860002404079,3,100,0.1,5
+spreading_maxsave,0.13702339999144897,5,100,0.1,5
+heuristic_maxsave,0.0499644999508746,5,100,0.1,5
+spreading_maxsave,0.15495280001778156,7,100,0.1,5
+heuristic_maxsave,0.04423040000256151,7,100,0.1,5
+spreading_maxsave,0.1916928999708034,10,100,0.1,5
+heuristic_maxsave,0.04138439998496324,10,100,0.1,5
+spreading_maxsave,0.06430410000029951,1,100,0.1,9
+heuristic_maxsave,0.025437000032979995,1,100,0.1,6
+spreading_maxsave,0.13984530000016093,2,100,0.1,12
+heuristic_maxsave,0.03264219994889572,2,100,0.1,9
+spreading_maxsave,0.10051050002221018,3,100,0.1,12
+heuristic_maxsave,0.038937399978749454,3,100,0.1,12
+spreading_maxsave,0.13558080000802875,5,100,0.1,13
+heuristic_maxsave,0.05305609997594729,5,100,0.1,16
+spreading_maxsave,0.24316899996483698,7,100,0.1,15
+heuristic_maxsave,0.06414859998039901,7,100,0.1,17
+spreading_maxsave,0.23131400003330782,10,100,0.1,17
+heuristic_maxsave,0.06319100002292544,10,100,0.1,17
+spreading_maxsave,0.05988299997989088,1,100,0.1,6
+heuristic_maxsave,0.02577399997971952,1,100,0.1,6
+spreading_maxsave,0.07544829999096692,2,100,0.1,9
+heuristic_maxsave,0.03426980000222102,2,100,0.1,9
+spreading_maxsave,0.09296229999745265,3,100,0.1,9
+heuristic_maxsave,0.12324909999733791,3,100,0.1,9
+spreading_maxsave,0.14677549997577444,5,100,0.1,9
+heuristic_maxsave,0.0495435000048019,5,100,0.1,9
+spreading_maxsave,0.1772472999873571,7,100,0.1,9
+heuristic_maxsave,0.055875000020023435,7,100,0.1,9
+spreading_maxsave,0.2268023999640718,10,100,0.1,9
+heuristic_maxsave,0.05596740002511069,10,100,0.1,9
+spreading_maxsave,0.06244779995176941,1,100,0.1,15
+heuristic_maxsave,0.025558800029102713,1,100,0.1,15
+spreading_maxsave,0.14300390001153573,2,100,0.1,22
+heuristic_maxsave,0.04185989999677986,2,100,0.1,20
+spreading_maxsave,0.14189980004448444,3,100,0.1,28
+heuristic_maxsave,0.07025290001183748,3,100,0.1,25
+spreading_maxsave,0.19750859995838255,5,100,0.1,33
+heuristic_maxsave,0.048199000011663884,5,100,0.1,32
+spreading_maxsave,0.23970649996772408,7,100,0.1,35
+heuristic_maxsave,0.07180949999019504,7,100,0.1,38
+spreading_maxsave,0.3098434999701567,10,100,0.1,38
+heuristic_maxsave,0.04116299998713657,10,100,0.1,39
+spreading_maxsave,0.06702149996999651,1,100,0.1,8
+heuristic_maxsave,0.024725899973418564,1,100,0.1,7
+spreading_maxsave,0.07488119998015463,2,100,0.1,12
+heuristic_maxsave,0.03541030001360923,2,100,0.1,9
+spreading_maxsave,0.10977509996155277,3,100,0.1,12
+heuristic_maxsave,0.03487839997978881,3,100,0.1,13
+spreading_maxsave,0.14335279999068007,5,100,0.1,13
+heuristic_maxsave,0.04845410003326833,5,100,0.1,13
+spreading_maxsave,0.22635160002391785,7,100,0.1,13
+heuristic_maxsave,0.04644229996483773,7,100,0.1,13
+spreading_maxsave,0.19589239999186248,10,100,0.1,13
+heuristic_maxsave,0.04726169997593388,10,100,0.1,13
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+spreading_maxsave,0.7680094999959692,3,400.0,0.8,40
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+spreading_maxsave,0.6728860000148416,3,400.0,0.8,17
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+spreading_maxsave,0.9196489000460132,5,400.0,0.8,19
+heuristic_maxsave,0.8112997999996878,5,400.0,0.8,19
+spreading_maxsave,1.0027675000019372,7,400.0,0.8,21
+heuristic_maxsave,1.032043799990788,7,400.0,0.8,21
+spreading_maxsave,1.082156100019347,10,400.0,0.8,24
+heuristic_maxsave,1.66049690003274,10,400.0,0.8,24
diff --git a/experiments/firefighter_problem/spreading_minbudget.csv b/experiments/firefighter_problem/spreading_minbudget.csv
new file mode 100644
index 0000000..7c2b261
--- /dev/null
+++ b/experiments/firefighter_problem/spreading_minbudget.csv
@@ -0,0 +1,20 @@
+algorithm,runtime,graph_nodes,Budget
+spreading_minbudget,0.4963123999768868,100,"(4, [(89, 1), (47, 1), (84, 1), (30, 1), (38, 2), (50, 2), (3, 2), (26, 2)])"
+heuristic_minbudget,0.12413459992967546,100,"(4, [(47, 1), (92, 1), (44, 1), (17, 1), (83, 2), (62, 2), (50, 2), (26, 2), (69, 3), (29, 3)])"
+spreading_minbudget,0.39317540009506047,100,"(11, [(3, 1), (15, 1), (28, 1), (54, 1), (71, 1), (96, 1), (97, 1), (17, 1), (35, 1), (45, 1), (22, 1)])"
+heuristic_minbudget,1.0460371000226587,100,"(10, [(22, 1), (35, 1), (28, 1), (54, 1), (96, 1), (17, 1), (97, 1), (15, 1), (45, 1), (71, 1)])"
+spreading_minbudget,0.2668848999310285,100,"(14, [(14, 1), (20, 1), (30, 1), (40, 1), (48, 1), (57, 1), (71, 1), (80, 1), (86, 1), (91, 1), (92, 1), (96, 1), (5, 1), (89, 1)])"
+heuristic_minbudget,3.6302230999572203,100,"(14, [(14, 1), (40, 1), (48, 1), (86, 1), (96, 1), (20, 1), (91, 1), (80, 1), (92, 1), (71, 1), (30, 1), (5, 1), (57, 1), (89, 1)])"
+spreading_minbudget,1.212209300021641,200,"(22, [(70, 1), (128, 1), (53, 1), (55, 1), (125, 1), (152, 1), (28, 1), (104, 1), (17, 1), (20, 1), (174, 1), (5, 1), (31, 1), (35, 1), (44, 1), (120, 1), (151, 1), (172, 1), (175, 1), (190, 1), (146, 1), (168, 1)])"
+heuristic_minbudget,1.0129838000284508,200,"(14, [(174, 1), (151, 1), (146, 1), (168, 1), (17, 1), (172, 1), (152, 1), (190, 1), (35, 1), (5, 1), (44, 1), (175, 1), (120, 1), (52, 1), (128, 2), (109, 2), (148, 2), (16, 2), (76, 2), (32, 2), (114, 2), (8, 2), (95, 2), (39, 2), (48, 2), (138, 2), (116, 2), (157, 2)])"
+spreading_minbudget,0.5931069999933243,200,"(5, [(5, 1), (44, 1), (193, 1), (170, 1), (24, 1)])"
+heuristic_minbudget,5.592074999934994,200,"(4, [(44, 1), (24, 1), (193, 1), (170, 1)])"
+spreading_minbudget,1.2939483999507502,200,"(40, [(89, 1), (3, 1), (4, 1), (13, 1), (17, 1), (19, 1), (27, 1), (45, 1), (50, 1), (62, 1), (74, 1), (84, 1), (92, 1), (95, 1), (97, 1), (118, 1), (119, 1), (123, 1), (124, 1), (128, 1), (138, 1), (142, 1), (144, 1), (146, 1), (152, 1), (153, 1), (180, 1), (191, 1), (198, 1), (11, 1), (29, 1), (93, 1), (100, 1), (141, 1), (164, 1), (167, 1), (173, 1), (184, 1), (102, 1), (86, 1)])"
+heuristic_minbudget,20.179923600051552,200,"(40, [(4, 1), (146, 1), (144, 1), (153, 1), (152, 1), (62, 1), (173, 1), (119, 1), (13, 1), (89, 1), (142, 1), (164, 1), (27, 1), (45, 1), (102, 1), (95, 1), (141, 1), (128, 1), (29, 1), (167, 1), (86, 1), (191, 1), (74, 1), (100, 1), (11, 1), (84, 1), (3, 1), (118, 1), (93, 1), (180, 1), (92, 1), (50, 1), (138, 1), (17, 1), (184, 1), (19, 1), (124, 1), (123, 1), (198, 1), (97, 1)])"
+spreading_minbudget,3.5869039999088272,400,"(21, [(69, 1), (116, 1), (239, 1), (159, 1), (250, 1), (37, 1), (192, 1), (144, 1), (387, 1), (29, 1), (287, 1), (7, 1), (63, 1), (300, 1), (305, 1), (93, 1), (280, 1), (112, 1), (149, 1), (11, 1), (230, 1)])"
+heuristic_minbudget,2.8195147999795154,400,"(15, [(287, 1), (305, 1), (300, 1), (149, 1), (63, 1), (11, 1), (93, 1), (280, 1), (112, 1), (230, 1), (29, 1), (343, 1), (103, 1), (364, 1), (339, 1), (190, 2), (110, 2), (121, 2), (393, 2), (193, 2), (200, 2), (354, 2), (1, 2), (147, 2), (159, 2), (367, 2), (267, 2), (204, 2), (50, 2), (373, 2)])"
+spreading_minbudget,6.544073999975808,400,"(63, [(103, 1), (333, 1), (88, 1), (2, 1), (17, 1), (27, 1), (29, 1), (66, 1), (72, 1), (76, 1), (89, 1), (135, 1), (143, 1), (148, 1), (150, 1), (152, 1), (165, 1), (166, 1), (190, 1), (222, 1), (250, 1), (257, 1), (275, 1), (289, 1), (291, 1), (292, 1), (293, 1), (306, 1), (315, 1), (326, 1), (327, 1), (363, 1), (373, 1), (380, 1), (386, 1), (40, 1), (109, 1), (112, 1), (140, 1), (182, 1), (229, 1), (238, 1), (239, 1), (325, 1), (390, 1), (9, 1), (90, 1), (171, 1), (184, 1), (359, 1), (385, 1), (393, 1), (11, 1), (51, 1), (71, 1), (212, 1), (364, 1), (230, 1), (368, 1), (391, 1), (52, 1), (353, 1), (276, 1)])"
+heuristic_minbudget,45.2434607000323,400,"(62, [(327, 1), (150, 1), (364, 1), (166, 1), (291, 1), (143, 1), (229, 1), (315, 1), (17, 1), (109, 1), (212, 1), (27, 1), (2, 1), (11, 1), (257, 1), (306, 1), (148, 1), (239, 1), (390, 1), (363, 1), (71, 1), (76, 1), (275, 1), (276, 1), (72, 1), (184, 1), (325, 1), (353, 1), (51, 1), (135, 1), (112, 1), (165, 1), (238, 1), (293, 1), (289, 1), (385, 1), (9, 1), (140, 1), (222, 1), (250, 1), (386, 1), (359, 1), (29, 1), (373, 1), (292, 1), (391, 1), (326, 1), (40, 1), (380, 1), (171, 1), (230, 1), (393, 1), (182, 1), (368, 1), (52, 1), (66, 1), (152, 1), (88, 1), (89, 1), (333, 1), (190, 1), (90, 1)])"
+spreading_minbudget,4.017668400076218,400,"(43, [(44, 1), (56, 1), (71, 1), (104, 1), (105, 1), (110, 1), (130, 1), (142, 1), (151, 1), (157, 1), (171, 1), (179, 1), (189, 1), (214, 1), (222, 1), (229, 1), (232, 1), (271, 1), (281, 1), (296, 1), (297, 1), (308, 1), (309, 1), (335, 1), (339, 1), (344, 1), (354, 1), (355, 1), (359, 1), (371, 1), (373, 1), (382, 1), (385, 1), (68, 1), (89, 1), (98, 1), (150, 1), (253, 1), (254, 1), (307, 1), (369, 1), (378, 1), (84, 1)])"
+heuristic_minbudget,96.92596789996605,400,"(43, [(56, 1), (84, 1), (222, 1), (214, 1), (307, 1), (335, 1), (369, 1), (371, 1), (309, 1), (339, 1), (104, 1), (189, 1), (229, 1), (232, 1), (382, 1), (296, 1), (130, 1), (151, 1), (171, 1), (110, 1), (179, 1), (271, 1), (71, 1), (344, 1), (354, 1), (378, 1), (254, 1), (385, 1), (68, 1), (157, 1), (281, 1), (308, 1), (44, 1), (373, 1), (105, 1), (359, 1), (142, 1), (253, 1), (297, 1), (150, 1), (355, 1), (89, 1), (98, 1)])"
+,195.34563290001824,,
diff --git a/experiments/firefighter_problem/spreading_minbudget.png b/experiments/firefighter_problem/spreading_minbudget.png
new file mode 100644
index 0000000..a42e7c2
Binary files /dev/null and b/experiments/firefighter_problem/spreading_minbudget.png differ
diff --git a/experiments/firefighter_problem/spreading_minbudget_preprocessed.csv b/experiments/firefighter_problem/spreading_minbudget_preprocessed.csv
new file mode 100644
index 0000000..48b6414
--- /dev/null
+++ b/experiments/firefighter_problem/spreading_minbudget_preprocessed.csv
@@ -0,0 +1,19 @@
+algorithm,runtime,graph_nodes,Budget,Budget_numeric
+spreading_minbudget,0.4963123999768868,100.0,"(4, [(89, 1), (47, 1), (84, 1), (30, 1), (38, 2), (50, 2), (3, 2), (26, 2)])",4.0
+heuristic_minbudget,0.1241345999296754,100.0,"(4, [(47, 1), (92, 1), (44, 1), (17, 1), (83, 2), (62, 2), (50, 2), (26, 2), (69, 3), (29, 3)])",4.0
+spreading_minbudget,0.3931754000950604,100.0,"(11, [(3, 1), (15, 1), (28, 1), (54, 1), (71, 1), (96, 1), (97, 1), (17, 1), (35, 1), (45, 1), (22, 1)])",11.0
+heuristic_minbudget,1.0460371000226587,100.0,"(10, [(22, 1), (35, 1), (28, 1), (54, 1), (96, 1), (17, 1), (97, 1), (15, 1), (45, 1), (71, 1)])",10.0
+spreading_minbudget,0.2668848999310285,100.0,"(14, [(14, 1), (20, 1), (30, 1), (40, 1), (48, 1), (57, 1), (71, 1), (80, 1), (86, 1), (91, 1), (92, 1), (96, 1), (5, 1), (89, 1)])",14.0
+heuristic_minbudget,3.63022309995722,100.0,"(14, [(14, 1), (40, 1), (48, 1), (86, 1), (96, 1), (20, 1), (91, 1), (80, 1), (92, 1), (71, 1), (30, 1), (5, 1), (57, 1), (89, 1)])",14.0
+spreading_minbudget,1.212209300021641,200.0,"(22, [(70, 1), (128, 1), (53, 1), (55, 1), (125, 1), (152, 1), (28, 1), (104, 1), (17, 1), (20, 1), (174, 1), (5, 1), (31, 1), (35, 1), (44, 1), (120, 1), (151, 1), (172, 1), (175, 1), (190, 1), (146, 1), (168, 1)])",22.0
+heuristic_minbudget,1.0129838000284508,200.0,"(14, [(174, 1), (151, 1), (146, 1), (168, 1), (17, 1), (172, 1), (152, 1), (190, 1), (35, 1), (5, 1), (44, 1), (175, 1), (120, 1), (52, 1), (128, 2), (109, 2), (148, 2), (16, 2), (76, 2), (32, 2), (114, 2), (8, 2), (95, 2), (39, 2), (48, 2), (138, 2), (116, 2), (157, 2)])",14.0
+spreading_minbudget,0.5931069999933243,200.0,"(5, [(5, 1), (44, 1), (193, 1), (170, 1), (24, 1)])",5.0
+heuristic_minbudget,5.592074999934994,200.0,"(4, [(44, 1), (24, 1), (193, 1), (170, 1)])",4.0
+spreading_minbudget,1.2939483999507502,200.0,"(40, [(89, 1), (3, 1), (4, 1), (13, 1), (17, 1), (19, 1), (27, 1), (45, 1), (50, 1), (62, 1), (74, 1), (84, 1), (92, 1), (95, 1), (97, 1), (118, 1), (119, 1), (123, 1), (124, 1), (128, 1), (138, 1), (142, 1), (144, 1), (146, 1), (152, 1), (153, 1), (180, 1), (191, 1), (198, 1), (11, 1), (29, 1), (93, 1), (100, 1), (141, 1), (164, 1), (167, 1), (173, 1), (184, 1), (102, 1), (86, 1)])",40.0
+heuristic_minbudget,20.179923600051552,200.0,"(40, [(4, 1), (146, 1), (144, 1), (153, 1), (152, 1), (62, 1), (173, 1), (119, 1), (13, 1), (89, 1), (142, 1), (164, 1), (27, 1), (45, 1), (102, 1), (95, 1), (141, 1), (128, 1), (29, 1), (167, 1), (86, 1), (191, 1), (74, 1), (100, 1), (11, 1), (84, 1), (3, 1), (118, 1), (93, 1), (180, 1), (92, 1), (50, 1), (138, 1), (17, 1), (184, 1), (19, 1), (124, 1), (123, 1), (198, 1), (97, 1)])",40.0
+spreading_minbudget,3.5869039999088272,400.0,"(21, [(69, 1), (116, 1), (239, 1), (159, 1), (250, 1), (37, 1), (192, 1), (144, 1), (387, 1), (29, 1), (287, 1), (7, 1), (63, 1), (300, 1), (305, 1), (93, 1), (280, 1), (112, 1), (149, 1), (11, 1), (230, 1)])",21.0
+heuristic_minbudget,2.819514799979516,400.0,"(15, [(287, 1), (305, 1), (300, 1), (149, 1), (63, 1), (11, 1), (93, 1), (280, 1), (112, 1), (230, 1), (29, 1), (343, 1), (103, 1), (364, 1), (339, 1), (190, 2), (110, 2), (121, 2), (393, 2), (193, 2), (200, 2), (354, 2), (1, 2), (147, 2), (159, 2), (367, 2), (267, 2), (204, 2), (50, 2), (373, 2)])",15.0
+spreading_minbudget,6.544073999975808,400.0,"(63, [(103, 1), (333, 1), (88, 1), (2, 1), (17, 1), (27, 1), (29, 1), (66, 1), (72, 1), (76, 1), (89, 1), (135, 1), (143, 1), (148, 1), (150, 1), (152, 1), (165, 1), (166, 1), (190, 1), (222, 1), (250, 1), (257, 1), (275, 1), (289, 1), (291, 1), (292, 1), (293, 1), (306, 1), (315, 1), (326, 1), (327, 1), (363, 1), (373, 1), (380, 1), (386, 1), (40, 1), (109, 1), (112, 1), (140, 1), (182, 1), (229, 1), (238, 1), (239, 1), (325, 1), (390, 1), (9, 1), (90, 1), (171, 1), (184, 1), (359, 1), (385, 1), (393, 1), (11, 1), (51, 1), (71, 1), (212, 1), (364, 1), (230, 1), (368, 1), (391, 1), (52, 1), (353, 1), (276, 1)])",63.0
+heuristic_minbudget,45.2434607000323,400.0,"(62, [(327, 1), (150, 1), (364, 1), (166, 1), (291, 1), (143, 1), (229, 1), (315, 1), (17, 1), (109, 1), (212, 1), (27, 1), (2, 1), (11, 1), (257, 1), (306, 1), (148, 1), (239, 1), (390, 1), (363, 1), (71, 1), (76, 1), (275, 1), (276, 1), (72, 1), (184, 1), (325, 1), (353, 1), (51, 1), (135, 1), (112, 1), (165, 1), (238, 1), (293, 1), (289, 1), (385, 1), (9, 1), (140, 1), (222, 1), (250, 1), (386, 1), (359, 1), (29, 1), (373, 1), (292, 1), (391, 1), (326, 1), (40, 1), (380, 1), (171, 1), (230, 1), (393, 1), (182, 1), (368, 1), (52, 1), (66, 1), (152, 1), (88, 1), (89, 1), (333, 1), (190, 1), (90, 1)])",62.0
+spreading_minbudget,4.017668400076218,400.0,"(43, [(44, 1), (56, 1), (71, 1), (104, 1), (105, 1), (110, 1), (130, 1), (142, 1), (151, 1), (157, 1), (171, 1), (179, 1), (189, 1), (214, 1), (222, 1), (229, 1), (232, 1), (271, 1), (281, 1), (296, 1), (297, 1), (308, 1), (309, 1), (335, 1), (339, 1), (344, 1), (354, 1), (355, 1), (359, 1), (371, 1), (373, 1), (382, 1), (385, 1), (68, 1), (89, 1), (98, 1), (150, 1), (253, 1), (254, 1), (307, 1), (369, 1), (378, 1), (84, 1)])",43.0
+heuristic_minbudget,96.92596789996604,400.0,"(43, [(56, 1), (84, 1), (222, 1), (214, 1), (307, 1), (335, 1), (369, 1), (371, 1), (309, 1), (339, 1), (104, 1), (189, 1), (229, 1), (232, 1), (382, 1), (296, 1), (130, 1), (151, 1), (171, 1), (110, 1), (179, 1), (271, 1), (71, 1), (344, 1), (354, 1), (378, 1), (254, 1), (385, 1), (68, 1), (157, 1), (281, 1), (308, 1), (44, 1), (373, 1), (105, 1), (359, 1), (142, 1), (253, 1), (297, 1), (150, 1), (355, 1), (89, 1), (98, 1)])",43.0
diff --git a/experiments/spreading_minbudget.csv b/experiments/spreading_minbudget.csv
new file mode 100644
index 0000000..ab7013e
--- /dev/null
+++ b/experiments/spreading_minbudget.csv
@@ -0,0 +1,114 @@
+algorithm,runtime,graph_nodes,edge_probability,Budget
+spreading_minbudget,0.6043815999873914,100,0.1,"(4, [(6, 1), (23, 1), (27, 1), (25, 1)])"
+heuristic_minbudget,0.08351690000563394,100,0.1,"(2, [(25, 1), (6, 1), (27, 2), (23, 2), (41, 3), (72, 3)])"
+spreading_minbudget,0.798920300003374,100,0.1,"(3, [(94, 1), (6, 1), (76, 1), (79, 2), (16, 2), (99, 2)])"
+heuristic_minbudget,0.0549452000122983,100,0.1,"(3, [(6, 1), (19, 1), (85, 1), (18, 2), (87, 2), (17, 2), (81, 3)])"
+spreading_minbudget,1.2247725000052014,100,0.1,"(7, [(6, 1), (70, 1), (23, 1), (36, 1), (47, 1), (2, 1), (25, 1)])"
+heuristic_minbudget,0.20194240000273567,100,0.1,"(4, [(47, 1), (25, 1), (19, 1), (85, 1), (17, 2), (96, 2), (61, 2), (67, 2), (42, 3)])"
+spreading_minbudget,0.5262910000019474,100,0.1,"(1, [(26, 1), (52, 2)])"
+heuristic_minbudget,0.09640729999227915,100,0.1,"(2, [(19, 1), (14, 1), (52, 2), (76, 2), (22, 3), (60, 3)])"
+spreading_minbudget,1.2042019000073196,100,0.1,"(6, [(72, 1), (91, 1), (16, 1), (14, 1), (38, 1), (25, 1)])"
+heuristic_minbudget,0.12059449999651406,100,0.1,"(4, [(14, 1), (25, 1), (19, 1), (47, 1), (90, 2), (65, 2), (91, 2), (21, 2), (42, 3), (70, 3)])"
+spreading_minbudget,0.1407623999984935,100,0.1,"(1, [(6, 1)])"
+heuristic_minbudget,0.07592089999525342,100,0.1,"(1, [(6, 1), (84, 2)])"
+spreading_minbudget,1.4573968000040622,100,0.1,"(6, [(9, 1), (13, 1), (19, 1), (23, 1), (3, 1), (47, 1)])"
+heuristic_minbudget,0.07776210000156425,100,0.1,"(4, [(19, 1), (47, 1), (6, 1), (85, 1), (78, 2), (87, 2), (71, 2), (39, 2)])"
+spreading_minbudget,0.8562765999959083,100,0.1,"(3, [(30, 1), (10, 1), (11, 1), (33, 2), (1, 2), (55, 2)])"
+heuristic_minbudget,0.05599090000032447,100,0.1,"(3, [(6, 1), (85, 1), (14, 1), (11, 2), (89, 2), (78, 2), (69, 3)])"
+spreading_minbudget,0.5544522999989567,100,0.1,"(1, [(6, 1), (78, 2)])"
+heuristic_minbudget,0.09719980000227224,100,0.1,"(2, [(25, 1), (6, 1), (93, 2), (11, 2), (72, 3), (64, 3)])"
+spreading_minbudget,0.4506552999955602,100,0.1,"(2, [(6, 1), (2, 1), (84, 2), (1, 2)])"
+heuristic_minbudget,0.08434780000243336,100,0.1,"(2, [(6, 1), (19, 1), (84, 2), (17, 2), (72, 3), (69, 3)])"
+spreading_minbudget,2.9608414999966044,100,0.5,"(29, [(54, 1), (37, 1), (9, 1), (11, 1), (12, 1), (23, 1), (31, 1), (46, 1), (60, 1), (61, 1), (88, 1), (90, 1), (2, 1), (15, 1), (24, 1), (27, 1), (45, 1), (62, 1), (20, 1), (26, 1), (32, 1), (86, 1), (94, 1), (97, 1), (28, 1), (66, 1), (93, 1), (13, 1), (65, 1)])"
+heuristic_minbudget,2.033734099997673,100,0.5,"(29, [(37, 1), (45, 1), (65, 1), (12, 1), (46, 1), (88, 1), (24, 1), (54, 1), (93, 1), (28, 1), (26, 1), (13, 1), (60, 1), (62, 1), (31, 1), (61, 1), (27, 1), (90, 1), (2, 1), (9, 1), (23, 1), (20, 1), (66, 1), (94, 1), (97, 1), (15, 1), (86, 1), (32, 1), (11, 1)])"
+spreading_minbudget,2.7890169999882346,100,0.5,"(24, [(31, 1), (38, 1), (16, 1), (46, 1), (48, 1), (61, 1), (82, 1), (84, 1), (98, 1), (2, 1), (15, 1), (45, 1), (54, 1), (62, 1), (64, 1), (77, 1), (79, 1), (85, 1), (26, 1), (32, 1), (34, 1), (78, 1), (28, 1), (93, 1)])"
+heuristic_minbudget,1.3695207999990089,100,0.5,"(22, [(85, 1), (98, 1), (54, 1), (84, 1), (46, 1), (28, 1), (45, 1), (48, 1), (15, 1), (26, 1), (93, 1), (34, 1), (61, 1), (62, 1), (79, 1), (82, 1), (16, 1), (78, 1), (2, 1), (32, 1), (77, 1), (64, 1)])"
+spreading_minbudget,0.29501640000671614,100,0.5,"(2, [(34, 1), (82, 1)])"
+heuristic_minbudget,0.8983767999889096,100,0.5,"(2, [(34, 1), (82, 1)])"
+spreading_minbudget,1.612422099991818,100,0.5,"(16, [(60, 1), (9, 1), (11, 1), (30, 1), (46, 1), (90, 1), (2, 1), (15, 1), (29, 1), (37, 1), (77, 1), (85, 1), (52, 1), (78, 1), (28, 1), (13, 1)])"
+heuristic_minbudget,1.2286775999964448,100,0.5,"(16, [(52, 1), (28, 1), (85, 1), (29, 1), (37, 1), (46, 1), (13, 1), (60, 1), (90, 1), (2, 1), (30, 1), (15, 1), (78, 1), (9, 1), (77, 1), (11, 1)])"
+spreading_minbudget,1.9392723999917507,100,0.5,"(18, [(58, 1), (22, 1), (46, 1), (48, 1), (61, 1), (2, 1), (19, 1), (37, 1), (64, 1), (77, 1), (79, 1), (85, 1), (32, 1), (72, 1), (78, 1), (28, 1), (66, 1), (13, 1)])"
+heuristic_minbudget,1.2242184999922756,100,0.5,"(17, [(22, 1), (72, 1), (13, 1), (37, 1), (46, 1), (28, 1), (48, 1), (61, 1), (85, 1), (19, 1), (32, 1), (78, 1), (2, 1), (79, 1), (77, 1), (66, 1), (64, 1)])"
+spreading_minbudget,2.1627451999956975,100,0.5,"(19, [(67, 1), (7, 1), (9, 1), (11, 1), (31, 1), (88, 1), (90, 1), (91, 1), (17, 1), (37, 1), (45, 1), (62, 1), (64, 1), (20, 1), (22, 1), (72, 1), (97, 1), (92, 1), (65, 1)])"
+heuristic_minbudget,1.7830877999949735,100,0.5,"(17, [(88, 1), (22, 1), (91, 1), (37, 1), (45, 1), (65, 1), (20, 1), (31, 1), (9, 1), (72, 1), (90, 1), (17, 1), (62, 1), (92, 1), (11, 1), (97, 1), (64, 1)])"
+spreading_minbudget,3.6650694999989355,100,0.5,"(29, [(30, 1), (46, 1), (11, 1), (12, 1), (16, 1), (41, 1), (61, 1), (82, 1), (84, 1), (88, 1), (98, 1), (2, 1), (15, 1), (24, 1), (27, 1), (45, 1), (77, 1), (79, 1), (85, 1), (22, 1), (43, 1), (72, 1), (74, 1), (78, 1), (86, 1), (97, 1), (92, 1), (13, 1), (65, 1)])"
+heuristic_minbudget,2.367954000001191,100,0.5,"(29, [(98, 1), (85, 1), (24, 1), (84, 1), (46, 1), (88, 1), (22, 1), (12, 1), (27, 1), (65, 1), (45, 1), (41, 1), (61, 1), (72, 1), (13, 1), (2, 1), (43, 1), (79, 1), (86, 1), (92, 1), (15, 1), (30, 1), (77, 1), (82, 1), (97, 1), (11, 1), (16, 1), (74, 1), (78, 1)])"
+spreading_minbudget,1.6317382999986876,100,0.5,"(13, [(12, 1), (7, 1), (11, 1), (16, 1), (88, 1), (15, 1), (19, 1), (27, 1), (54, 1), (20, 1), (26, 1), (43, 1), (28, 1)])"
+heuristic_minbudget,1.2327431000012439,100,0.5,"(13, [(27, 1), (20, 1), (88, 1), (12, 1), (28, 1), (54, 1), (26, 1), (7, 1), (43, 1), (15, 1), (19, 1), (16, 1), (11, 1)])"
+spreading_minbudget,1.377598899998702,100,0.5,"(9, [(23, 1), (82, 1), (30, 1), (40, 1), (62, 1), (79, 1), (85, 1), (22, 1), (92, 1)])"
+heuristic_minbudget,1.0871489999990445,100,0.5,"(8, [(85, 1), (79, 1), (82, 1), (40, 1), (22, 1), (62, 1), (30, 1), (92, 1)])"
+spreading_minbudget,1.249198300007265,100,0.5,"(12, [(31, 1), (16, 1), (41, 1), (84, 1), (90, 1), (24, 1), (29, 1), (37, 1), (40, 1), (85, 1), (13, 1), (65, 1)])"
+heuristic_minbudget,1.291403099996387,100,0.5,"(11, [(84, 1), (29, 1), (37, 1), (40, 1), (24, 1), (85, 1), (65, 1), (41, 1), (13, 1), (90, 1), (16, 1)])"
+spreading_minbudget,0.8987213000073098,100,0.8,"(8, [(84, 1), (16, 1), (21, 1), (68, 1), (86, 1), (87, 1), (44, 1), (52, 1)])"
+heuristic_minbudget,2.5706658999988576,100,0.8,"(8, [(52, 1), (84, 1), (21, 1), (87, 1), (16, 1), (86, 1), (44, 1), (68, 1)])"
+spreading_minbudget,0.5972516000038013,100,0.8,"(7, [(19, 1), (6, 1), (24, 1), (42, 1), (66, 1), (71, 1), (72, 1)])"
+heuristic_minbudget,2.627842400004738,100,0.8,"(7, [(24, 1), (6, 1), (71, 1), (19, 1), (66, 1), (72, 1), (42, 1)])"
+spreading_minbudget,2.4423267999954987,100,0.8,"(25, [(22, 1), (1, 1), (6, 1), (8, 1), (9, 1), (23, 1), (25, 1), (27, 1), (42, 1), (51, 1), (56, 1), (58, 1), (63, 1), (72, 1), (76, 1), (79, 1), (86, 1), (93, 1), (4, 1), (15, 1), (33, 1), (34, 1), (41, 1), (44, 1), (11, 1)])"
+heuristic_minbudget,3.5214248999982374,100,0.8,"(25, [(27, 1), (76, 1), (6, 1), (4, 1), (25, 1), (58, 1), (34, 1), (51, 1), (9, 1), (8, 1), (22, 1), (11, 1), (15, 1), (23, 1), (33, 1), (44, 1), (56, 1), (86, 1), (93, 1), (1, 1), (79, 1), (41, 1), (63, 1), (72, 1), (42, 1)])"
+spreading_minbudget,2.2762453999894205,100,0.8,"(23, [(21, 1), (2, 1), (8, 1), (9, 1), (16, 1), (22, 1), (29, 1), (37, 1), (48, 1), (53, 1), (65, 1), (71, 1), (76, 1), (85, 1), (86, 1), (89, 1), (91, 1), (95, 1), (96, 1), (97, 1), (98, 1), (74, 1), (94, 1)])"
+heuristic_minbudget,3.9915353000105824,100,0.8,"(23, [(76, 1), (2, 1), (48, 1), (98, 1), (9, 1), (29, 1), (21, 1), (22, 1), (91, 1), (37, 1), (16, 1), (65, 1), (8, 1), (71, 1), (85, 1), (89, 1), (86, 1), (94, 1), (74, 1), (97, 1), (95, 1), (53, 1), (96, 1)])"
+spreading_minbudget,3.2877872999961255,100,0.8,"(33, [(69, 1), (1, 1), (2, 1), (6, 1), (8, 1), (10, 1), (12, 1), (22, 1), (23, 1), (24, 1), (25, 1), (27, 1), (29, 1), (31, 1), (37, 1), (43, 1), (45, 1), (46, 1), (48, 1), (53, 1), (58, 1), (65, 1), (66, 1), (67, 1), (82, 1), (89, 1), (95, 1), (98, 1), (4, 1), (33, 1), (41, 1), (52, 1), (94, 1)])"
+heuristic_minbudget,4.246031399990898,100,0.8,"(33, [(6, 1), (4, 1), (25, 1), (48, 1), (2, 1), (24, 1), (52, 1), (58, 1), (27, 1), (69, 1), (22, 1), (37, 1), (29, 1), (94, 1), (43, 1), (46, 1), (65, 1), (82, 1), (98, 1), (89, 1), (8, 1), (45, 1), (10, 1), (66, 1), (12, 1), (23, 1), (33, 1), (41, 1), (1, 1), (31, 1), (67, 1), (53, 1), (95, 1)])"
+spreading_minbudget,2.8299892999930307,100,0.8,"(27, [(5, 1), (1, 1), (6, 1), (8, 1), (9, 1), (20, 1), (27, 1), (31, 1), (37, 1), (46, 1), (51, 1), (53, 1), (55, 1), (58, 1), (63, 1), (64, 1), (66, 1), (73, 1), (79, 1), (81, 1), (83, 1), (85, 1), (91, 1), (98, 1), (41, 1), (44, 1), (18, 1)])"
+heuristic_minbudget,4.0879720999946585,100,0.8,"(27, [(58, 1), (6, 1), (51, 1), (20, 1), (98, 1), (27, 1), (64, 1), (8, 1), (9, 1), (73, 1), (46, 1), (37, 1), (5, 1), (83, 1), (55, 1), (41, 1), (81, 1), (18, 1), (31, 1), (91, 1), (53, 1), (1, 1), (63, 1), (44, 1), (85, 1), (66, 1), (79, 1)])"
+spreading_minbudget,3.92984680000518,100,0.8,"(41, [(16, 1), (1, 1), (2, 1), (10, 1), (13, 1), (19, 1), (23, 1), (24, 1), (27, 1), (29, 1), (32, 1), (39, 1), (46, 1), (51, 1), (53, 1), (56, 1), (59, 1), (62, 1), (64, 1), (66, 1), (67, 1), (68, 1), (77, 1), (79, 1), (82, 1), (85, 1), (87, 1), (89, 1), (93, 1), (95, 1), (96, 1), (98, 1), (99, 1), (33, 1), (34, 1), (41, 1), (44, 1), (94, 1), (11, 1), (40, 1), (18, 1)])"
+heuristic_minbudget,3.953235400011181,100,0.8,"(41, [(67, 1), (39, 1), (34, 1), (24, 1), (2, 1), (40, 1), (51, 1), (82, 1), (29, 1), (27, 1), (46, 1), (87, 1), (64, 1), (56, 1), (16, 1), (19, 1), (23, 1), (53, 1), (94, 1), (10, 1), (98, 1), (66, 1), (1, 1), (44, 1), (33, 1), (11, 1), (13, 1), (18, 1), (32, 1), (59, 1), (93, 1), (85, 1), (41, 1), (79, 1), (89, 1), (62, 1), (68, 1), (95, 1), (96, 1), (77, 1), (99, 1)])"
+spreading_minbudget,1.3322335999982897,100,0.8,"(14, [(6, 1), (1, 1), (22, 1), (29, 1), (46, 1), (58, 1), (69, 1), (75, 1), (77, 1), (82, 1), (85, 1), (92, 1), (95, 1), (40, 1)])"
+heuristic_minbudget,2.7363971000013407,100,0.8,"(14, [(6, 1), (40, 1), (58, 1), (29, 1), (82, 1), (69, 1), (22, 1), (46, 1), (92, 1), (85, 1), (77, 1), (1, 1), (75, 1), (95, 1)])"
+spreading_minbudget,0.8161610999959521,100,0.8,"(8, [(22, 1), (31, 1), (45, 1), (85, 1), (86, 1), (91, 1), (96, 1), (44, 1)])"
+heuristic_minbudget,2.7852620000048773,100,0.8,"(8, [(45, 1), (22, 1), (91, 1), (31, 1), (86, 1), (44, 1), (85, 1), (96, 1)])"
+spreading_minbudget,1.302543899990269,100,0.8,"(14, [(2, 1), (10, 1), (45, 1), (63, 1), (64, 1), (65, 1), (79, 1), (85, 1), (91, 1), (92, 1), (96, 1), (52, 1), (74, 1), (40, 1)])"
+heuristic_minbudget,4.053526600007899,100,0.8,"(14, [(2, 1), (40, 1), (52, 1), (64, 1), (65, 1), (91, 1), (45, 1), (92, 1), (10, 1), (74, 1), (85, 1), (63, 1), (79, 1), (96, 1)])"
+spreading_minbudget,6.874619900001562,200,0.1,"(13, [(48, 1), (24, 1), (157, 1), (42, 1), (196, 1), (33, 1), (21, 1), (59, 1), (153, 1), (28, 1), (52, 1), (136, 1), (99, 1)])"
+heuristic_minbudget,0.3828627999901073,200,0.1,"(8, [(99, 1), (52, 1), (153, 1), (136, 1), (28, 1), (48, 1), (147, 1), (194, 1), (92, 2), (91, 2), (50, 2), (1, 2), (186, 2), (82, 2), (42, 2), (178, 2)])"
+spreading_minbudget,3.6053887000016402,200,0.1,"(8, [(116, 1), (153, 1), (45, 1), (49, 1), (105, 1), (95, 1), (65, 1), (99, 1)])"
+heuristic_minbudget,0.43296489999920595,200,0.1,"(5, [(99, 1), (65, 1), (153, 1), (194, 1), (76, 1), (64, 2), (29, 2), (91, 2), (168, 2), (80, 2)])"
+spreading_minbudget,6.127774299995508,200,0.1,"(12, [(57, 1), (164, 1), (21, 1), (49, 1), (108, 1), (194, 1), (11, 1), (42, 1), (68, 1), (153, 1), (65, 1), (28, 1)])"
+heuristic_minbudget,0.5014686999929836,200,0.1,"(8, [(194, 1), (153, 1), (28, 1), (65, 1), (106, 1), (48, 1), (52, 1), (76, 1), (29, 2), (177, 2), (142, 2), (171, 2), (178, 2), (120, 2), (16, 2), (128, 2)])"
+spreading_minbudget,6.081753100006608,200,0.1,"(14, [(155, 1), (131, 1), (185, 1), (6, 1), (44, 1), (76, 1), (147, 1), (153, 1), (79, 1), (161, 1), (28, 1), (112, 1), (52, 1), (106, 1)])"
+heuristic_minbudget,0.3598169000033522,200,0.1,"(8, [(147, 1), (153, 1), (52, 1), (76, 1), (106, 1), (112, 1), (28, 1), (48, 1), (192, 2), (3, 2), (101, 2), (22, 2), (122, 2), (78, 2), (195, 2), (17, 2)])"
+spreading_minbudget,6.416437199994107,200,0.1,"(10, [(194, 1), (6, 1), (52, 1), (101, 1), (4, 1), (170, 1), (46, 1), (9, 1), (41, 1), (28, 1)])"
+heuristic_minbudget,0.5401426000025822,200,0.1,"(8, [(52, 1), (4, 1), (28, 1), (194, 1), (106, 1), (147, 1), (76, 1), (48, 1), (17, 2), (2, 2), (61, 2), (50, 2), (115, 2), (143, 2), (16, 2), (93, 2)])"
+spreading_minbudget,7.155516500002705,200,0.1,"(13, [(124, 1), (196, 1), (116, 1), (66, 1), (21, 1), (120, 1), (128, 1), (138, 1), (44, 1), (72, 1), (48, 1), (65, 1), (136, 1)])"
+heuristic_minbudget,0.45384590000321623,200,0.1,"(9, [(48, 1), (44, 1), (136, 1), (65, 1), (147, 1), (52, 1), (194, 1), (76, 1), (106, 1), (170, 2), (184, 2), (12, 2), (50, 2), (2, 2), (57, 2), (129, 2), (87, 2), (69, 2)])"
+spreading_minbudget,5.644121200006339,200,0.1,"(13, [(129, 1), (199, 1), (44, 1), (82, 1), (39, 1), (76, 1), (182, 1), (194, 1), (54, 1), (161, 1), (4, 1), (28, 1), (52, 1)])"
+heuristic_minbudget,0.48520840000128374,200,0.1,"(9, [(194, 1), (76, 1), (52, 1), (4, 1), (28, 1), (161, 1), (147, 1), (48, 1), (44, 1), (17, 2), (107, 2), (57, 2), (129, 2), (122, 2), (81, 2), (108, 2), (121, 2), (2, 2)])"
+spreading_minbudget,1.8839236000058008,200,0.1,"(5, [(48, 1), (91, 1), (42, 1), (136, 1), (106, 1)])"
+heuristic_minbudget,0.398219099995913,200,0.1,"(3, [(136, 1), (106, 1), (48, 1), (157, 2), (128, 2), (120, 2)])"
+spreading_minbudget,8.769554500002414,200,0.1,"(16, [(3, 1), (157, 1), (116, 1), (106, 1), (70, 1), (44, 1), (17, 1), (43, 1), (138, 1), (194, 1), (147, 1), (76, 1), (4, 1), (48, 1), (65, 1), (112, 1)])"
+heuristic_minbudget,0.48429249999753665,200,0.1,"(10, [(48, 1), (147, 1), (194, 1), (76, 1), (106, 1), (44, 1), (65, 1), (112, 1), (4, 1), (52, 1), (142, 2), (16, 2), (107, 2), (69, 2), (42, 2), (12, 2), (143, 2), (87, 2), (6, 2), (177, 2)])"
+spreading_minbudget,4.215613599997596,200,0.1,"(9, [(116, 1), (33, 1), (70, 1), (101, 1), (21, 1), (194, 1), (4, 1), (52, 1), (106, 1)])"
+heuristic_minbudget,0.4958438000030583,200,0.1,"(6, [(52, 1), (106, 1), (4, 1), (147, 1), (194, 1), (76, 1), (59, 2), (81, 2), (2, 2), (129, 2), (61, 2), (16, 2)])"
+spreading_minbudget,0.1568801999965217,200,0.5,"(1, [(10, 1)])"
+heuristic_minbudget,3.0877527999982703,200,0.5,"(1, [(132, 1)])"
+spreading_minbudget,2.236697499989532,200,0.5,"(6, [(99, 1), (168, 1), (175, 1), (31, 1), (149, 1), (177, 1)])"
+heuristic_minbudget,3.3113985999953,200,0.5,"(5, [(149, 1), (168, 1), (177, 1), (31, 1), (175, 1)])"
+spreading_minbudget,9.140447199999471,200,0.5,"(32, [(59, 1), (144, 1), (63, 1), (19, 1), (34, 1), (41, 1), (50, 1), (65, 1), (82, 1), (85, 1), (103, 1), (116, 1), (130, 1), (143, 1), (168, 1), (180, 1), (184, 1), (191, 1), (193, 1), (28, 1), (75, 1), (139, 1), (146, 1), (149, 1), (162, 1), (61, 1), (68, 1), (81, 1), (137, 1), (186, 1), (153, 1), (192, 1)])"
+heuristic_minbudget,5.723877700002049,200,0.5,"(31, [(184, 1), (143, 1), (116, 1), (61, 1), (59, 1), (149, 1), (130, 1), (186, 1), (75, 1), (68, 1), (82, 1), (103, 1), (162, 1), (191, 1), (193, 1), (41, 1), (19, 1), (180, 1), (192, 1), (28, 1), (85, 1), (50, 1), (168, 1), (63, 1), (34, 1), (137, 1), (153, 1), (146, 1), (65, 1), (139, 1), (81, 1)])"
+spreading_minbudget,2.4964694999944186,200,0.5,"(8, [(63, 1), (85, 1), (140, 1), (180, 1), (193, 1), (197, 1), (199, 1), (119, 1)])"
+heuristic_minbudget,3.2830257000023266,200,0.5,"(7, [(180, 1), (140, 1), (193, 1), (119, 1), (199, 1), (85, 1), (197, 1)])"
+spreading_minbudget,1.0909339999925578,200,0.5,"(2, [(4, 1), (192, 1)])"
+heuristic_minbudget,3.0061140000034356,200,0.5,"(2, [(192, 1), (108, 1)])"
+spreading_minbudget,2.8638310999958776,200,0.5,"(9, [(31, 1), (13, 1), (41, 1), (45, 1), (103, 1), (116, 1), (74, 1), (127, 1), (68, 1)])"
+heuristic_minbudget,3.336111199998413,200,0.5,"(7, [(45, 1), (41, 1), (116, 1), (68, 1), (103, 1), (127, 1), (74, 1)])"
+spreading_minbudget,6.566627099993639,200,0.5,"(19, [(1, 1), (76, 1), (34, 1), (112, 1), (160, 1), (193, 1), (197, 1), (55, 1), (69, 1), (86, 1), (122, 1), (139, 1), (141, 1), (159, 1), (196, 1), (137, 1), (16, 1), (153, 1), (93, 1)])"
+heuristic_minbudget,4.1070819000015035,200,0.5,"(17, [(86, 1), (139, 1), (193, 1), (122, 1), (196, 1), (69, 1), (93, 1), (159, 1), (55, 1), (153, 1), (112, 1), (34, 1), (141, 1), (137, 1), (16, 1), (160, 1), (197, 1)])"
+spreading_minbudget,11.145615999994334,200,0.5,"(35, [(99, 1), (138, 1), (48, 1), (32, 1), (44, 1), (52, 1), (56, 1), (85, 1), (103, 1), (107, 1), (120, 1), (130, 1), (140, 1), (160, 1), (175, 1), (180, 1), (191, 1), (8, 1), (25, 1), (55, 1), (67, 1), (69, 1), (74, 1), (86, 1), (132, 1), (139, 1), (141, 1), (159, 1), (68, 1), (98, 1), (104, 1), (186, 1), (177, 1), (119, 1), (21, 1)])"
+heuristic_minbudget,6.92385840001225,200,0.5,"(33, [(103, 1), (67, 1), (68, 1), (130, 1), (132, 1), (48, 1), (186, 1), (177, 1), (69, 1), (21, 1), (191, 1), (98, 1), (104, 1), (107, 1), (119, 1), (180, 1), (32, 1), (140, 1), (159, 1), (85, 1), (120, 1), (86, 1), (175, 1), (52, 1), (8, 1), (55, 1), (25, 1), (139, 1), (160, 1), (56, 1), (44, 1), (141, 1), (74, 1)])"
+spreading_minbudget,7.714225499992608,200,0.5,"(27, [(194, 1), (30, 1), (19, 1), (41, 1), (56, 1), (65, 1), (85, 1), (87, 1), (115, 1), (116, 1), (121, 1), (130, 1), (140, 1), (143, 1), (168, 1), (175, 1), (180, 1), (181, 1), (17, 1), (67, 1), (122, 1), (138, 1), (141, 1), (196, 1), (68, 1), (81, 1), (104, 1)])"
+heuristic_minbudget,4.569759200006956,200,0.5,"(26, [(30, 1), (138, 1), (121, 1), (130, 1), (41, 1), (116, 1), (67, 1), (196, 1), (68, 1), (87, 1), (19, 1), (168, 1), (17, 1), (104, 1), (115, 1), (180, 1), (85, 1), (143, 1), (140, 1), (175, 1), (181, 1), (122, 1), (56, 1), (65, 1), (141, 1), (81, 1)])"
+spreading_minbudget,5.409246000010171,200,0.5,"(21, [(184, 1), (34, 1), (45, 1), (52, 1), (80, 1), (103, 1), (112, 1), (120, 1), (130, 1), (143, 1), (168, 1), (175, 1), (193, 1), (199, 1), (8, 1), (28, 1), (109, 1), (135, 1), (198, 1), (61, 1), (119, 1)])"
+heuristic_minbudget,4.488193300014245,200,0.5,"(21, [(184, 1), (45, 1), (193, 1), (61, 1), (130, 1), (119, 1), (103, 1), (199, 1), (80, 1), (52, 1), (28, 1), (120, 1), (143, 1), (175, 1), (34, 1), (135, 1), (168, 1), (8, 1), (109, 1), (112, 1), (198, 1)])"
+spreading_minbudget,5.363142900008825,200,0.8,"(21, [(3, 1), (21, 1), (33, 1), (44, 1), (45, 1), (68, 1), (69, 1), (70, 1), (74, 1), (138, 1), (149, 1), (150, 1), (155, 1), (171, 1), (176, 1), (179, 1), (195, 1), (198, 1), (37, 1), (162, 1), (190, 1)])"
+heuristic_minbudget,13.136786300005042,200,0.8,"(21, [(195, 1), (171, 1), (150, 1), (155, 1), (44, 1), (3, 1), (45, 1), (74, 1), (69, 1), (190, 1), (68, 1), (179, 1), (149, 1), (37, 1), (162, 1), (21, 1), (138, 1), (70, 1), (198, 1), (176, 1), (33, 1)])"
+spreading_minbudget,13.20309090000228,200,0.8,"(63, [(17, 1), (6, 1), (13, 1), (16, 1), (21, 1), (22, 1), (23, 1), (25, 1), (26, 1), (28, 1), (33, 1), (35, 1), (36, 1), (38, 1), (39, 1), (43, 1), (53, 1), (58, 1), (60, 1), (61, 1), (65, 1), (68, 1), (70, 1), (71, 1), (73, 1), (77, 1), (78, 1), (88, 1), (90, 1), (99, 1), (108, 1), (109, 1), (113, 1), (124, 1), (129, 1), (131, 1), (134, 1), (136, 1), (140, 1), (142, 1), (148, 1), (150, 1), (155, 1), (163, 1), (175, 1), (176, 1), (178, 1), (179, 1), (184, 1), (192, 1), (195, 1), (196, 1), (198, 1), (199, 1), (5, 1), (8, 1), (15, 1), (29, 1), (63, 1), (95, 1), (123, 1), (133, 1), (146, 1)])"
+heuristic_minbudget,18.206225700007053,200,0.8,"(63, [(53, 1), (26, 1), (88, 1), (5, 1), (23, 1), (38, 1), (150, 1), (155, 1), (178, 1), (39, 1), (108, 1), (134, 1), (13, 1), (36, 1), (163, 1), (17, 1), (109, 1), (175, 1), (195, 1), (63, 1), (113, 1), (8, 1), (77, 1), (71, 1), (124, 1), (136, 1), (140, 1), (21, 1), (148, 1), (22, 1), (43, 1), (60, 1), (123, 1), (142, 1), (65, 1), (6, 1), (35, 1), (196, 1), (68, 1), (95, 1), (176, 1), (179, 1), (28, 1), (146, 1), (29, 1), (58, 1), (70, 1), (61, 1), (25, 1), (73, 1), (78, 1), (199, 1), (133, 1), (33, 1), (99, 1), (131, 1), (90, 1), (184, 1), (198, 1), (15, 1), (129, 1), (16, 1), (192, 1)])"
+spreading_minbudget,1.1575602000084473,200,0.8,"(5, [(80, 1), (28, 1), (86, 1), (134, 1), (195, 1)])"
+heuristic_minbudget,9.099992300005397,200,0.8,"(5, [(80, 1), (134, 1), (28, 1), (195, 1), (86, 1)])"
+spreading_minbudget,8.297417900001165,200,0.8,"(33, [(26, 1), (19, 1), (25, 1), (30, 1), (31, 1), (35, 1), (42, 1), (61, 1), (72, 1), (76, 1), (78, 1), (93, 1), (94, 1), (98, 1), (125, 1), (128, 1), (132, 1), (134, 1), (135, 1), (138, 1), (140, 1), (155, 1), (163, 1), (172, 1), (178, 1), (195, 1), (196, 1), (81, 1), (133, 1), (146, 1), (27, 1), (51, 1), (59, 1)])"
+heuristic_minbudget,13.201126400002977,200,0.8,"(33, [(26, 1), (19, 1), (94, 1), (59, 1), (155, 1), (178, 1), (128, 1), (81, 1), (134, 1), (163, 1), (27, 1), (195, 1), (72, 1), (98, 1), (31, 1), (42, 1), (132, 1), (30, 1), (76, 1), (196, 1), (140, 1), (125, 1), (25, 1), (51, 1), (93, 1), (135, 1), (61, 1), (138, 1), (146, 1), (35, 1), (133, 1), (78, 1), (172, 1)])"
+spreading_minbudget,12.984143499998027,200,0.8,"(63, [(89, 1), (3, 1), (13, 1), (14, 1), (16, 1), (17, 1), (23, 1), (32, 1), (33, 1), (38, 1), (40, 1), (41, 1), (42, 1), (45, 1), (47, 1), (56, 1), (58, 1), (64, 1), (65, 1), (67, 1), (68, 1), (75, 1), (76, 1), (80, 1), (86, 1), (90, 1), (92, 1), (93, 1), (98, 1), (99, 1), (100, 1), (106, 1), (112, 1), (117, 1), (121, 1), (131, 1), (132, 1), (134, 1), (136, 1), (142, 1), (150, 1), (151, 1), (158, 1), (164, 1), (171, 1), (174, 1), (175, 1), (183, 1), (187, 1), (188, 1), (196, 1), (197, 1), (198, 1), (199, 1), (5, 1), (8, 1), (52, 1), (95, 1), (96, 1), (102, 1), (116, 1), (123, 1), (87, 1)])"
+heuristic_minbudget,17.87442839999858,200,0.8,"(63, [(175, 1), (5, 1), (171, 1), (89, 1), (23, 1), (102, 1), (40, 1), (38, 1), (150, 1), (47, 1), (151, 1), (197, 1), (13, 1), (52, 1), (17, 1), (41, 1), (75, 1), (96, 1), (76, 1), (65, 1), (56, 1), (80, 1), (116, 1), (132, 1), (134, 1), (8, 1), (98, 1), (67, 1), (136, 1), (42, 1), (58, 1), (174, 1), (86, 1), (32, 1), (121, 1), (164, 1), (3, 1), (196, 1), (95, 1), (112, 1), (68, 1), (64, 1), (131, 1), (100, 1), (123, 1), (142, 1), (187, 1), (117, 1), (188, 1), (14, 1), (45, 1), (199, 1), (198, 1), (16, 1), (106, 1), (33, 1), (87, 1), (158, 1), (92, 1), (99, 1), (90, 1), (93, 1), (183, 1)])"
+spreading_minbudget,5.6764264999947045,200,0.8,"(27, [(66, 1), (6, 1), (16, 1), (25, 1), (31, 1), (38, 1), (41, 1), (57, 1), (65, 1), (76, 1), (89, 1), (92, 1), (106, 1), (126, 1), (140, 1), (158, 1), (160, 1), (167, 1), (174, 1), (182, 1), (185, 1), (192, 1), (196, 1), (52, 1), (95, 1), (102, 1), (181, 1)])"
+heuristic_minbudget,13.88039399999252,200,0.8,"(27, [(76, 1), (185, 1), (66, 1), (89, 1), (102, 1), (38, 1), (174, 1), (65, 1), (6, 1), (52, 1), (182, 1), (167, 1), (41, 1), (196, 1), (25, 1), (126, 1), (140, 1), (95, 1), (31, 1), (181, 1), (16, 1), (92, 1), (158, 1), (57, 1), (160, 1), (106, 1), (192, 1)])"
+spreading_minbudget,4.208028399996692,200,0.8,"(16, [(31, 1), (13, 1), (38, 1), (58, 1), (75, 1), (76, 1), (78, 1), (88, 1), (98, 1), (101, 1), (153, 1), (164, 1), (167, 1), (197, 1), (63, 1), (159, 1)])"
diff --git a/networkz/algorithms/approximation/firefighter_problem/Firefighter_Problem.py b/networkz/algorithms/approximation/firefighter_problem/Firefighter_Problem.py
new file mode 100644
index 0000000..4a3703b
--- /dev/null
+++ b/networkz/algorithms/approximation/firefighter_problem/Firefighter_Problem.py
@@ -0,0 +1,524 @@
+"""
+The Paper - 
+Approximability of the Firefighter Problem Computing Cuts over Time
+
+Paper Link -
+https://www.math.uwaterloo.ca/~cswamy/papers/firefighter-journ.pdf
+
+Authors - 
+Elliot Anshelevich
+Deeparnab Chakrabarty
+Ameya Hate 
+Chaitanya Swamy
+
+Developers - 
+Yuval Bubnovsky
+Almog David
+Shaked Levi
+    
+"""
+
+import networkx as nx
+import networkx.algorithms.connectivity as algo 
+import math
+import logging
+from networkz.algorithms.max_flow_with_node_capacity import min_cut_with_node_capacity
+from networkz.algorithms.approximation.firefighter_problem.Utils import *
+
+def setup_logger(logger):
+    logger.setLevel(logging.INFO)
+    
+    console_handler = logging.StreamHandler()
+    console_handler.setLevel(logging.INFO)
+    
+    formatter = logging.Formatter('%(asctime)s - %(levelname)s - %(message)s')
+    console_handler.setFormatter(formatter)
+    
+    logger.addHandler(console_handler)
+    return logger
+
+logger = logging.getLogger('firefighter_problem_main')
+
+
+def spreading_maxsave(Graph:nx.DiGraph, budget:int, source:int, targets:list, stop_condition=None) -> tuple[list, set]:    
+    """
+    Approximate the firefighter problem by maximizing the number of saved nodes.
+
+    Parameters:
+    ----------
+    Graph : nx.DiGraph
+        Directed graph representing the network.
+    budget : int
+        Number of nodes that can be vaccinated at each time step.
+    source : int
+        Source node where the infection starts.
+    targets : list
+        List of target nodes to be saved.
+    stop_condition : optional
+        If set, stops early if all targets are saved or if any target is infected.
+
+    Returns:
+    -------
+    tuple:
+        vaccination_strategy : list
+            List of tuples representing the vaccination strategy.
+        saved_target_nodes : set
+            Set of nodes that are saved from infection.
+
+    Examples:
+    --------
+    Example 1:
+    >>> G = nx.DiGraph()
+    >>> G.add_nodes_from([0,1,2], status="vulnerable")
+    >>> G.add_edges_from([(0,1),(0,2),(1,2)])
+    >>> spreading_maxsave(G,1,0,[1,2])
+    ([(1, 1)], {1})
+
+    Example 2:
+    >>> G1 = nx.DiGraph()
+    >>> G1.add_nodes_from([0,1,2,3], status="vulnerable")
+    >>> G1.add_edges_from([(0,1),(0,2),(1,2),(1,3),(2,3)])
+    >>> spreading_maxsave(G1,1,0,[1,2,3])
+    ([(1, 1)], {1, 3})
+
+    Example 3:
+    >>> G2 = nx.DiGraph()
+    >>> G2.add_nodes_from([0,1,2,3,4,5,6], status="vulnerable")
+    >>> G2.add_edges_from([(0,1),(0,2),(1,2),(1,4),(2,3),(2,6),(3,5)])
+    >>> spreading_maxsave(G2,1,0,[1,2,3,4,5,6])
+    ([(2, 1), (4, 2)], {2, 3, 4, 5, 6})
+
+    Example 4:
+    >>> G3 = nx.DiGraph() 
+    >>> G3.add_nodes_from([0,1,2,3,4,5,6,7,8], status="vulnerable")
+    >>> G3.add_edges_from([(0,2),(0,4),(0,5),(2,1),(2,3),(4,1),(4,6),(5,3),(5,6),(5,7),(6,7),(6,8),(7,8)])
+    >>> spreading_maxsave(G3,2,0,[1,2,3,4,5,6,7,8])
+    ([(5, 1), (2, 1), (8, 2)], {1, 2, 3, 5, 6, 7, 8})
+    """
+
+    if budget < 1:
+        logger.critical("Error: The budget must be at least 1")
+        raise ValueError("Error: The budget must be at least 1")
+        
+    validate_parameters(Graph, source, targets)
+    logger.info(f"Starting the spreading_maxsave function with source node {source}, budget {budget}, and targets: {targets}")
+    
+    clean_graph(Graph)
+    local_targets = targets.copy()
+    infected_nodes = []
+    vaccinated_nodes = []
+    vaccination_strategy = []
+    saved_target_nodes = set()
+    can_spread = True
+    Graph.nodes[source]['status'] = Status.INFECTED.value
+    infected_nodes.append(source)
+    
+    logger.info("Calculating all possible direct vaccinations in each timestamp")
+    gamma, direct_vaccinations = calculate_gamma(Graph, source, targets)
+    
+    logger.info("Calculating direct vaccinations grouping by timestamp")
+    epsilon = calculate_epsilon(direct_vaccinations)
+    
+    time_step = 0
+    while can_spread and time_step < len(epsilon):
+        spread_vaccination(Graph, vaccinated_nodes)
+        for i in range(budget):
+            logger.info(f"Calculating the best direct vaccination strategy for the current time step that saves more new nodes in targets (Current budget: {i+1} out of {budget})")
+            vaccination, nodes_saved = find_best_direct_vaccination(Graph, direct_vaccinations, epsilon[time_step], local_targets)
+            
+            if vaccination != ():
+                logger.info(f"Found {vaccination} as a solution for current timestamp. Appending to vaccination strategy and vaccinating the node")
+                vaccination_strategy.append(vaccination)
+                
+                chosen_node = vaccination[0]
+                vaccinate_node(Graph, chosen_node)
+                
+                vaccinated_nodes.append(chosen_node)
+                logger.info(f"Updated list of currently vaccinated nodes: {vaccinated_nodes}")
+
+                if nodes_saved is not None:
+                    saved_target_nodes.update(nodes_saved)
+                    local_targets[:] = [element for element in local_targets if element not in nodes_saved]
+                    logger.info(f"Updated list of targets: {local_targets}")
+
+            else:
+                logger.info(f"All nodes are either vaccinated or infected")
+                break
+
+        can_spread = spread_virus(Graph, infected_nodes)
+
+        if stop_condition is not None:
+            if len(local_targets) == 0 or any(node in infected_nodes for node in local_targets):
+                logger.info(f"Returning vaccination strategy: {vaccination_strategy}. The strategy saved the nodes: {saved_target_nodes}")
+                return vaccination_strategy, saved_target_nodes
+
+        time_step += 1
+
+    logger.info(f"Returning vaccination strategy: {vaccination_strategy}. The strategy saves the nodes: {saved_target_nodes}")
+    return vaccination_strategy, saved_target_nodes
+
+
+def spreading_minbudget(Graph:nx.DiGraph, source:int, targets:list) -> tuple[int, list]:
+    """
+    Approximate the firefighter problem by minimizing the budget required to save all target nodes.
+
+    Parameters:
+    ----------
+    Graph : nx.DiGraph
+        Directed graph representing the network.
+    source : int
+        Source node where the infection starts.
+    targets : list
+        List of target nodes to be saved.
+
+    Returns:
+    -------
+    tuple:
+        min_budget : int
+            Minimum budget required to save all target nodes.
+        best_strategy : list
+            List of tuples representing the vaccination strategy.
+
+    Examples:
+    --------
+    Example 1: 
+    >>> G1 = nx.DiGraph()
+    >>> G1.add_nodes_from([0,1,2,3], status="vulnerable")
+    >>> G1.add_edges_from([(0,1),(0,2),(1,2),(1,3),(2,3)])
+    >>> spreading_minbudget(G1,0,[1,2,3])
+    (2, [(1, 1), (2, 1)])
+
+    Example 2: 
+    >>> G1 = nx.DiGraph()
+    >>> G1.add_nodes_from([0,1,2,3], status="vulnerable")
+    >>> G1.add_edges_from([(0,1),(0,2),(1,2),(1,3),(2,3)])
+    >>> spreading_minbudget(G1,0,[1,3])
+    (1, [(1, 1)])
+
+    Example 3:
+    >>> G2 = nx.DiGraph()
+    >>> G2.add_nodes_from([0,1,2,3,4,5,6], status="vulnerable")
+    >>> G2.add_edges_from([(0,1),(0,2),(1,2),(1,4),(2,3),(2,6),(3,5)])
+    >>> spreading_minbudget(G2,0,[1,2,3,4,5,6])
+    (2, [(2, 1), (1, 1)])
+
+    Example 4:
+    >>> G3 = nx.DiGraph() 
+    >>> G3.add_nodes_from([0,1,2,3,4,5,6,7,8], status="vulnerable")
+    >>> G3.add_edges_from([(0,2),(0,4),(0,5),(2,1),(2,3),(4,1),(4,6),(5,3),(5,6),(5,7),(6,7),(6,8),(7,8)])
+    >>> spreading_minbudget(G3,0,[1,2,3,4,5,6,7,8])
+    (3, [(5, 1), (2, 1), (4, 1)])
+    """
+
+    validate_parameters(Graph, source, targets)
+    logger.info(f"Starting the spreading_minbudget function with source node {source} and targets: {targets}")
+
+    min_value = 1
+    max_value = len(targets)
+    min_budget = max_value
+    middle = math.floor((min_value + max_value) / 2)
+
+    best_strategy = spreading_maxsave(Graph, min_budget, source, targets, True)[0]
+
+    while min_value < max_value:
+        logger.info(f"Calling maxsave with parameters - Source: {source}, Targets: {targets}, Budget: {middle}")
+        strategy, nodes_saved = spreading_maxsave(Graph, middle, source, targets, True)
+        
+        common_elements = set(nodes_saved) & set(targets)
+
+        if len(common_elements) == len(targets):
+            logger.info(f"The current budget {middle} has saved all the targets!")
+            max_value = middle
+            if middle < min_budget:
+                min_budget = middle
+                best_strategy = strategy
+        else:
+            logger.info(f"The current budget {middle} didn't save all the targets!")
+            min_value = middle + 1
+
+        middle = math.floor((min_value + max_value) / 2)
+
+    logger.info(f"Returning minimum budget: {middle} and the vaccination strategy: {best_strategy}")
+    return min_budget, best_strategy
+
+    
+def non_spreading_minbudget(Graph:nx.DiGraph, source:int, targets:list) -> int:
+    """
+    Calculate the minimum budget required to save all target nodes in a non-spreading scenario.
+
+    Parameters:
+    ----------
+    Graph : nx.DiGraph
+        Directed graph representing the network.
+    source : int
+        Source node where the infection starts.
+    targets : list
+        List of target nodes to be saved.
+
+    Returns:
+    -------
+    min_budget : int
+        Minimum budget required to save all target nodes.
+
+    Examples:
+    --------
+    Example 1: 
+    >>> G1 = nx.DiGraph()
+    >>> G1.add_nodes_from([0,1,2,3], status="vulnerable")
+    >>> G1.add_edges_from([(0,1),(0,2),(1,2),(1,3),(2,3)])
+    >>> non_spreading_minbudget(G1,0,[1,3])
+    (2, [(1, 1), (3, 1)])
+
+    Example 2: 
+    >>> G1 = nx.DiGraph()
+    >>> G1.add_nodes_from([0,1,2,3], status="vulnerable")
+    >>> G1.add_edges_from([(0,1),(0,2),(1,2),(1,3),(2,3)])
+    >>> non_spreading_minbudget(G1,0,[1,2,3])
+    (2, [(1, 1), (2, 1)])
+
+    Example 3:
+    >>> G2 = nx.DiGraph()
+    >>> G2.add_nodes_from([0,1,2,3,4,5,6], status="vulnerable")
+    >>> G2.add_edges_from([(0,1),(0,2),(1,2),(1,4),(2,3),(2,6),(3,5)])
+    >>> non_spreading_minbudget(G2,0,[1,2,3,4,5,6])
+    (2, [(1, 1), (2, 1)])
+
+    Example 4:
+    >>> G3 = nx.DiGraph() 
+    >>> G3.add_nodes_from([0,1,2,3,4,5,6,7,8], status="vulnerable")
+    >>> G3.add_edges_from([(0,2),(0,4),(0,5),(2,1),(2,3),(4,1),(4,6),(5,3),(5,6),(5,7),(6,7),(6,8),(7,8)])
+    >>> non_spreading_minbudget(G3,0,[2,6,1,8])
+    (3, [(2, 1), (4, 1), (5, 1)])
+    """
+    validate_parameters(Graph, source, targets)
+    logger.info(f"Starting the non_spreading_minbudget function with source node {source} and targets: {targets}")
+
+    G = create_st_graph(Graph, targets, 't')
+    min_cut = algo.minimum_st_node_cut(G, source, 't')
+    logger.info(f"Minimum s-t node cut: {min_cut}")
+    min_budget = len(min_cut)
+    strategy = [(item, 1) for item in min_cut]
+
+    logger.info(f"Returning minimum budget: {min_budget}")
+    return min_budget, strategy
+
+def non_spreading_dirlaynet_minbudget(Graph:nx.DiGraph, source:int, targets:list) -> tuple[int, list]:
+    """
+    Calculate the minimum budget required to save all target nodes in a non-spreading directed layer network.
+
+    Parameters:
+    ----------
+    Graph : nx.DiGraph
+        Directed graph representing the network.
+    source : int
+        Source node where the infection starts.
+    targets : list
+        List of target nodes to be saved.
+
+    Returns:
+    -------
+    tuple:
+        min_budget : int
+            Minimum budget required to save all target nodes.
+        best_strategy : list
+            List of tuples representing the vaccination strategy.
+
+    Examples:
+    --------
+    Example 1:
+    >>> G4 = nx.DiGraph()
+    >>> G4.add_nodes_from([0,1,2,3,4,5], status="vulnerable")
+    >>> G4.add_edges_from([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)])
+    >>> non_spreading_dirlaynet_minbudget(G4,0,[1,2,3,4,5])
+    (2, [(1, 1), (2, 1)])
+    """
+
+    validate_parameters(Graph, source, targets)
+    if not is_dag(Graph):
+       logger.error("The graph is not a DAG graph, thus cannot run the algorithm")
+       return
+    
+    #display_graph(Graph)
+    logger.info(f"Starting the non_spreading_dirlaynet_minbudget function with source node {source} and targets: {targets}")
+
+    layers = adjust_nodes_capacity(Graph, source)
+    G = create_st_graph(Graph, targets, 't')
+    #display_graph(G)
+    G_reduction_min_cut = min_cut_with_node_capacity(G, source=source, target='t')
+    N_groups = min_cut_N_groups(G_reduction_min_cut,layers)
+    vacc_matrix = calculate_vaccine_matrix(layers, N_groups)
+    integer_matrix = matrix_to_integers_values(vacc_matrix)
+    min_budget = min_budget_calculation(vacc_matrix)
+    strategy = dirlay_vaccination_strategy(integer_matrix, N_groups)
+
+    logger.info(f"Returning minimum budget: {min_budget} and the vaccination strategy: {strategy}")
+    return min_budget, strategy
+
+def heuristic_maxsave(Graph:nx.DiGraph, budget:int, source:int, targets:list, spreading=True,  stop_condition=None) -> tuple[list, set]:
+    """
+    Approximate the firefighter problem by maximizing the number of saved nodes in our heuristic apprach.
+    The heuristic approach is based on the local search problem. 
+    
+    Parameters
+    ----------
+    Graph : nx.DiGraph
+        Directed graph representing the network.
+    budget : int
+        Number of nodes that can be vaccinated at each time step.
+    source : int
+        Source node where the infection starts.
+    targets : list
+        List of target nodes to be saved.
+    spreading : bool
+        If True, vaccination spreads to neighboring nodes.
+    stop_condition : optional
+        If set, stops early if all targets are saved or if any target is infected.
+    
+    Returns
+    -------
+    tuple:
+        vaccination_strategy : list
+            List of tuples representing the vaccination strategy.
+        saved_target_nodes : set
+            Set of saved target nodes.
+        
+    Examples
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_nodes_from([0, 1, 2, 3], status="vulnerable")
+    >>> G.add_edges_from([(0, 1), (0, 2), (1, 2), (1, 3)])
+    >>> heuristic_maxsave(G, 1, 0, [1, 2, 3])
+    ([(1, 1)], {1, 3})
+    """
+    
+    if budget < 1:
+        logger.critical("Error: The budget must be at least 1")
+        raise ValueError("Error: The budget must be at least 1")
+
+    validate_parameters(Graph, source, targets)
+    logger.info(f"Starting the heuristic_maxsave function with source node {source}, budget {budget}, targets: {targets}, and spreading: {spreading}")
+
+    clean_graph(Graph)
+    #display_graph(Graph)
+    local_targets = targets.copy()
+    infected_nodes = []
+    vaccinated_nodes = []
+    vaccination_strategy = []
+    saved_target_nodes = set()
+    can_spread = True
+    Graph.nodes[source]['status'] = Status.INFECTED.value
+    infected_nodes.append(source)
+    #display_graph(Graph)
+    time_step = 1
+
+    while can_spread:
+        if spreading:
+            spread_vaccination(Graph, vaccinated_nodes)
+        for i in range(budget):
+            logger.info(f"Calculating the best direct vaccination strategy for the current time step that saves more new node in targets (Current budget: {budget})")
+            node_to_vaccinate, nodes_saved = find_best_neighbor(Graph, infected_nodes, local_targets, targets)
+            if node_to_vaccinate is not None:
+                logger.info(f"Found {node_to_vaccinate} as a solution for current timestamp, appending to vaccination strategy and vaccinating the node")
+                vaccination_strategy.append((node_to_vaccinate, time_step))
+                vaccinate_node(Graph, node_to_vaccinate)
+                vaccinated_nodes.append(node_to_vaccinate)
+                logger.info(f"Updated list of currently vaccinated nodes: {vaccinated_nodes}")
+
+                if nodes_saved is not None:
+                    local_targets[:] = [element for element in local_targets if element not in nodes_saved]
+                    logger.info(f"Updated list of targets: {local_targets}")
+
+            else:
+                logger.info(f"All nodes are either vaccinated or infected")
+                break
+        
+        can_spread = spread_virus(Graph, infected_nodes)
+
+        if stop_condition is not None:
+            if len(local_targets) == 0 or any(node in infected_nodes for node in local_targets):
+                for node in targets:
+                    node_status = Graph.nodes[node]['status']
+                    if node_status != Status.INFECTED.value:
+                        saved_target_nodes.add(node)
+                logger.info(f"Returning vaccination strategy: {vaccination_strategy}. The strategy saved the nodes: {saved_target_nodes}")
+                return vaccination_strategy, saved_target_nodes
+
+        time_step += 1
+    
+    for node in targets:
+        node_status = Graph.nodes[node]['status']
+        if node_status != Status.INFECTED.value:
+            saved_target_nodes.add(node)
+
+    logger.info(f"Returning vaccination strategy: {vaccination_strategy}. The strategy saves the nodes: {saved_target_nodes}")
+    return vaccination_strategy, saved_target_nodes
+
+def heuristic_minbudget(Graph:nx.DiGraph, source:int, targets:list, spreading:bool) -> tuple[int, list]:
+    """
+    Calculate the minimum budget required to save all target nodes in our heuristic approach.
+
+   Parameters
+    ----------
+    Graph : nx.DiGraph
+        Directed graph representing the network.
+    source : int
+        Source node where the infection starts.
+    targets : list
+        List of target nodes to be saved.
+    spreading : bool
+        If True, vaccination spreads to neighboring nodes.
+    
+    Returns
+    -------
+    tuple:
+        min_budget : int
+            Minimum budget required to save all target nodes.
+        best_strategy : list
+            List of tuples representing the vaccination strategy.
+    
+    Examples
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_nodes_from([0, 1, 2, 3], status="vulnerable")
+    >>> G.add_edges_from([(0, 1), (0, 2), (1, 2), (1, 3)])
+    >>> heuristic_minbudget(G, 0, [1, 2, 3], True)
+    (2, [(1, 1), (2, 1)])
+    """
+    
+    validate_parameters(Graph, source, targets)
+    logger.info(f"Starting the heuristic_minbudget function with source node {source}, targets: {targets}, and spreading: {spreading}")
+
+    min_value = 1
+    max_value = len(list(Graph.successors(source)))
+    min_budget = max_value
+    middle = math.floor((min_value + max_value) / 2)
+
+    best_strategy = heuristic_maxsave(Graph, min_budget, source, targets, spreading, True)[0]
+
+    while min_value < max_value:
+        logger.info(f"Calling heuristic_maxsave with parameters - Source: {source}, Targets: {targets}, Budget: {middle}")
+        strategy, nodes_saved = heuristic_maxsave(Graph, middle, source, targets, spreading, True)
+
+        common_elements = set(nodes_saved) & set(targets)
+
+        if len(common_elements) == len(targets):
+            logger.info(f"The current budget {middle} has saved all the targets!")
+            max_value = middle
+            if middle < min_budget:
+                min_budget = middle
+                best_strategy = strategy
+        else:
+            logger.info(f"The current budget {middle} didn't save all the targets!")
+            min_value = middle + 1
+
+        middle = math.floor((min_value + max_value) / 2)
+
+    logger.info(f"Returning minimum budget: {middle} and the vaccination strategy: {best_strategy}")
+    
+    return min_budget, best_strategy
+
+if __name__ == "__main__":
+
+    import doctest
+    result = doctest.testmod(verbose=False)
+    print(f"Doctest results: {result}")
\ No newline at end of file
diff --git a/networkz/algorithms/approximation/firefighter_problem/Random_Graph_Generator.py b/networkz/algorithms/approximation/firefighter_problem/Random_Graph_Generator.py
new file mode 100644
index 0000000..309614f
--- /dev/null
+++ b/networkz/algorithms/approximation/firefighter_problem/Random_Graph_Generator.py
@@ -0,0 +1,105 @@
+"""
+
+The Paper - 
+Approximability of the Firefighter Problem Computing Cuts over Time
+
+Paper Link -
+https://www.math.uwaterloo.ca/~cswamy/papers/firefighter-journ.pdf
+
+Authors - 
+Elliot Anshelevich
+Deeparnab Chakrabarty
+Ameya Hate 
+Chaitanya Swamy
+
+Developers - 
+Yuval Bubnovsky
+Almog David
+Shaked Levi
+
+"""
+
+import logging
+import random
+import networkx as nx
+
+logger = logging.getLogger(__name__)
+
+def generate_random_DiGraph(
+    num_nodes: int = 100,
+    edge_probability: float = 0.1,
+    seed: int = None
+    ) -> nx.DiGraph:
+    
+    if seed is None:
+        seed = random.randint(0, 2**32 - 1)
+        logger.debug(f"Random generated seed: {seed}")
+    else:
+        logger.debug(f"Using provided seed: {seed}")
+    
+    random.seed(seed)
+    
+    G = nx.DiGraph()
+    G.add_nodes_from(range(num_nodes), status="target")
+    
+    edges = [
+        (source, target) 
+        for source in range(num_nodes) 
+        for target in range(num_nodes) 
+        if source != target and random.random() < edge_probability
+    ]
+    
+    G.add_edges_from(edges)
+    
+    return G
+
+
+#TODO : make this to receive paramaters
+def generate_random_layered_network():
+    """
+    Generates a directed layered network with a random number of layers and random nodes per layer.
+    
+    Returns:
+        G (networkx.DiGraph): Directed graph representing the layered network.
+    """
+    # Randomly decide the number of layers (between 2 and 3 for this example)
+    num_layers = random.randint(5, 10)
+    
+    # Randomly decide the number of nodes per layer (between 1 and 4 for this example)
+    nodes_per_layer = [random.randint(5, 30) for _ in range(num_layers)]
+    
+    G = nx.DiGraph()
+    node_id = 1  # Start node_id from 1 because 0 is the source
+    
+    # Initialize layer 0 with the source node
+    layers = [[0]]
+    G.add_node(0)
+    
+    # Create nodes layer by layer
+    for i in range(num_layers):
+        layer = [node_id + j for j in range(nodes_per_layer[i])]
+        layers.append(layer)
+        G.add_nodes_from(layer)
+        node_id += nodes_per_layer[i]
+
+    print("LAYERS->", layers)
+    
+    # Connect source node (0) to all nodes in layer 1
+    for node in layers[1]:
+        G.add_edge(0, node)
+    
+    # Create edges ensuring connectivity between consecutive layers
+    for i in range(1, num_layers):
+        for node in layers[i]:
+            # Connect each node in this layer to at least one node in the next layer
+            connected_nodes = random.sample(layers[i + 1], k=random.randint(1, len(layers[i + 1])))
+            for target in connected_nodes:
+                if target != node:  # Ensure no self-loop
+                    G.add_edge(node, target)
+        
+        for target in layers[i + 1]:
+            # Ensure each node in the next layer is connected to from at least one node in this layer
+            if not any(G.has_edge(source, target) for source in layers[i]):
+                G.add_edge(random.choice(layers[i]), target)
+    
+    return G
diff --git a/networkz/algorithms/approximation/firefighter_problem/Utils.py b/networkz/algorithms/approximation/firefighter_problem/Utils.py
new file mode 100644
index 0000000..c62ce68
--- /dev/null
+++ b/networkz/algorithms/approximation/firefighter_problem/Utils.py
@@ -0,0 +1,893 @@
+"""
+The Paper - 
+Approximability of the Firefighter Problem Computing Cuts over Time
+
+Paper Link -
+https://www.math.uwaterloo.ca/~cswamy/papers/firefighter-journ.pdf
+
+Authors - 
+Elliot Anshelevich
+Deeparnab Chakrabarty
+Ameya Hate 
+Chaitanya Swamy
+
+Developers - 
+Yuval Bubnovsky
+Almog David
+Shaked Levi
+"""
+
+import networkx as nx
+import networkx.algorithms.connectivity as algo 
+import matplotlib.pyplot as plt
+import numpy as np
+from enum import Enum
+import copy
+import logging
+import heapq
+
+class Status(Enum):
+    VULNERABLE = "vulnerable"
+    INFECTED = "infected"
+    VACCINATED = "vaccinated"
+    DIRECTLY_VACCINATED = "directly vaccinated"
+
+
+node_colors = {
+    'vulnerable': 'gray',
+    'infected': 'red',
+    'vaccinated': 'blue',
+    'directly vaccinated': 'green',
+    'default' : "#00FFD0"
+}
+logger = logging.getLogger(__name__)
+
+# ============================ Validation Functions ============================
+
+def validate_parameters(graph:nx.DiGraph, source:int, targets:list) -> None:
+    """
+    Validate the source and target nodes in the graph.
+
+    Parameters:
+    ----------
+    graph : nx.DiGraph
+        Directed graph.
+    source : int
+        Source node.
+    targets : list
+        List of target nodes to save.
+
+    Raises:
+    -------
+    ValueError
+        If the source node is not in the graph.
+        If the source node is in the targets list.
+        If any target node is not in the graph.
+
+    Examples:
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_nodes_from([1, 2, 3, 4])
+    >>> validate_parameters(G, 1, [2, 3])
+    >>> validate_parameters(G, 5, [2, 3])
+    Traceback (most recent call last):
+        ...
+    ValueError: Error: The source node isn't on the graph
+    >>> validate_parameters(G, 1, [1, 3])
+    Traceback (most recent call last):
+        ...
+    ValueError: Error: The source node can't be a part of the targets list, since the virus is spreading from the source
+    >>> validate_parameters(G, 1, [2, 5])
+    Traceback (most recent call last):
+        ...
+    ValueError: Error: Not all nodes in the targets list are on the graph.
+    """
+    graph_nodes = list(graph.nodes())
+    if source not in graph_nodes:
+        logger.critical("Error: The source node isn't on the graph")
+        raise ValueError("Error: The source node isn't on the graph")
+        
+    if source in targets:
+        logger.critical("Error: The source node can't be a part of the targets list, since the virus is spreading from the source")
+        raise ValueError("Error: The source node can't be a part of the targets list, since the virus is spreading from the source")
+        
+    if not all(node in graph_nodes for node in targets):
+        logger.critical("Error: Not all nodes in the targets list are on the graph.")
+        raise ValueError("Error: Not all nodes in the targets list are on the graph.")
+
+def is_st_layered_dag(graph: nx.DiGraph, s: any, t: any) -> bool: #TODO: make this work and incorporate into code
+    """
+    Validates if a given graph is an s-t directed layered network.
+
+    In an s-t directed l-layered network, the vertex set consists of 
+    V = (L0 := {s}) U L1 U ... U Ll U {t}, and all arcs except those 
+    entering t are from a vertex in some layer Li to a vertex in Li+1; 
+    arcs entering t may originate from any vertex other than t.
+
+    Parameters
+    ----------
+    graph : nx.DiGraph
+        Directed graph.
+    s : any
+        Source vertex.
+    t : any
+        Target vertex.
+
+    Returns
+    -------
+    bool
+        True if the graph is an s-t directed l-layered network, False otherwise.
+
+    Examples
+    --------
+    Example 1:
+    >>> G = nx.DiGraph()
+    >>> G.add_edges_from([(0, 1), (1, 2), (2, 3)])
+    >>> is_st_layered_dag(G, 0, 3)
+    True
+
+    Example 2:
+    >>> G = nx.DiGraph()
+    >>> G.add_edges_from([(0, 1), (1, 2), (2, 1), (2, 3)])
+    >>> is_st_layered_dag(G, 0, 3)
+    False
+    """
+    logger.info(f'Validating {graph} is an s-t directed layered network')
+    if not nx.is_directed_acyclic_graph(graph):
+        logger.error(f'{graph} is not DAG and therefore cannot be an s-t directed layered network!')
+        return False
+    
+    topo_sort = list(nx.topological_sort(graph))
+    logger.debug(f'Performing topological sort to determine an ordering of vertices\n Sorted:{topo_sort}')
+    
+    if topo_sort[0] != s or topo_sort[-1] != t:
+        logger.error(f'First node in topological sort is not "t" or last node is not "s"')
+        return False
+
+    # Assign layer indices based on topological sort
+    node_layers = {node: index for index, node in enumerate(topo_sort)}
+    
+    # Check if all edges (except those entering t) go from a lower layer to the next higher layer
+    for u, v in graph.edges():
+        if v != t and node_layers[u] + 1 != node_layers[v]:
+            logger.error(f'The edge {u},{v} is an edge that does not enter "t" but goes from a higher to a lower layer - violating the required property')
+            return False
+
+    return True
+
+def is_dag(graph:nx.DiGraph) -> bool:
+    """
+    Validates if a given graph is a Directed Acyclic Graph (DAG) using NetworkX.
+
+    Parameters:
+    ----------
+    graph : nx.DiGraph
+        Directed graph.
+
+    Returns:
+    -------
+    bool
+        True if the graph is a DAG, False otherwise.
+
+    Examples:
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_edges_from([(1, 2), (2, 3)])
+    >>> is_dag(G)
+    True
+    >>> G.add_edge(3, 1)
+    >>> is_dag(G)
+    False
+    """
+    return nx.is_directed_acyclic_graph(graph)
+
+# ============================ End Validation Functions ============================
+
+# ============================ Spreading Max-Save ============================
+def calculate_gamma(graph:nx.DiGraph, source:int, targets:list) -> dict:
+    """
+    Calculate Gamma and S(u,t) based on the calculation in the article.
+
+    Parameters:
+    ----------
+    graph : nx.DiGraph
+        Directed graph.
+    source : int
+        Source node.
+    targets : list
+        List of target nodes to save.
+
+    Returns:
+    -------
+    gamma : dict
+        Dictionary of vaccination options.
+    direct_vaccination : dict
+        Dictionary of direct vaccination strategies - S(u,t).
+
+    Examples:
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_edges_from([(1, 2), (2, 3), (1, 3)])
+    >>> G.nodes[1]['capacity'] = 10
+    >>> G.nodes[2]['capacity'] = 15
+    >>> G.nodes[3]['capacity'] = 20
+    >>> gamma, direct_vaccination = calculate_gamma(G, 1, [3])
+    >>> gamma
+    {2: [(2, 1)], 3: [(3, 1)]}
+    >>> direct_vaccination
+    {(2, 1): [], (3, 1): [3]}
+    """
+    
+    gamma = {}
+    direct_vaccination = {}
+    unreachable_nodes = []
+    path_length = dict(nx.all_pairs_shortest_path_length(graph))
+    for key in graph.nodes:
+        vaccination_options = []
+        for node in graph.nodes:
+                if path_length[source].get(key) is not None and path_length[node].get(key) is not None:
+                    s_to_v = path_length[source].get(key)
+                    u_to_v = path_length[node].get(key)
+                    max_time = s_to_v - u_to_v
+                    if max_time > 0:
+                        for i in range(1,max_time+1):
+                            option = (node,i)
+                            vaccination_options.append(option)
+                            if option not in direct_vaccination:
+                                direct_vaccination[option] = []
+                            if key in targets:
+                                direct_vaccination[option].append(key)
+
+        if not vaccination_options:
+            unreachable_nodes.append(key)
+        if key != source:                       
+            gamma[key] = vaccination_options
+
+    for strategy in direct_vaccination:
+        for node in unreachable_nodes:
+            if node in targets:
+                direct_vaccination[strategy].append(node)
+    
+    logger.info("Gamma is: " + str(gamma))
+    logger.info("S(u,t) is: " + str(direct_vaccination))
+    return gamma, direct_vaccination
+
+def calculate_epsilon(direct_vaccinations:dict) -> list:
+    """
+    Calculate Epsilon based on the calculation in the article.
+
+    Parameters:
+    ----------
+    direct_vaccinations : dict
+        Dictionary of direct vaccination strategies.
+
+    Returns:
+    -------
+    epsilon : list
+        List of direct vaccination groups by time step.
+
+    Examples:
+    --------
+    >>> direct_vaccinations = {(1, 1): [3], (2, 2): [4], (3, 1): [5]}
+    >>> calculate_epsilon(direct_vaccinations)
+    [[(1, 1), (3, 1)], [(2, 2)]]
+    """
+    from itertools import groupby
+    from operator import itemgetter
+
+    sorted_dict = sorted(direct_vaccinations, key=itemgetter(1))
+    epsilon = [list(group) for _, group in groupby(sorted_dict, key=itemgetter(1))]
+    
+    logger.info("Epsilon is: " + str(epsilon))
+    return epsilon
+
+def find_best_direct_vaccination(graph:nx.DiGraph, direct_vaccinations:dict, current_time_options:list, targets:list) -> tuple:
+    """
+    Find the best direct vaccination strategy for the current time step that saves more new nodes in targets.
+
+    Parameters:
+    ----------
+    graph : nx.DiGraph
+        Directed graph representing the network.
+    direct_vaccinations : dict
+        Dictionary of direct vaccination strategies.
+    current_time_options : list
+        List of current time step vaccination options.
+    targets : list
+        List of target nodes.
+
+    Returns:
+    -------
+    tuple
+        best_vaccination : tuple
+            Best direct vaccination option for the current time stamp.
+        nodes_saved : list    
+            List of the nodes who's been saved by this option.
+
+    Examples:
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_nodes_from([(1, {"status": 'vulnerable'}), (2, {"status": 'vulnerable'}), (3, {"status": 'vulnerable'})])
+    >>> direct_vaccinations = {(1, 1): [1], (2, 2): [2]}
+    >>> current_time_options = [(1, 1), (2, 2)]
+    >>> targets = [2]
+    >>> find_best_direct_vaccination(G, direct_vaccinations, current_time_options, targets)
+    ((2, 2), {2})
+    """
+    best_vaccination = () 
+    nodes_saved = []
+    common_elements = None
+    max_number = -1
+    for option in current_time_options:
+        if(graph.nodes[option[0]]['status'] == Status.VULNERABLE.value):
+            nodes_list = direct_vaccinations.get(option)
+            common_elements = set(nodes_list) & set(targets)
+            logger.debug(f"Direct vaccination: {option}, Nodes saved: {common_elements} (if set(), then it's empty)")
+            if len(common_elements) > max_number:
+                best_vaccination = option
+                nodes_saved = common_elements
+                max_number = len(common_elements)
+    
+    if best_vaccination != ():
+        logger.info("The best direct vaccination is: " + str(best_vaccination) + " and it saves nodes: " + str(nodes_saved))
+    return best_vaccination, nodes_saved
+
+def spread_virus(graph:nx.DiGraph, infected_nodes:list) -> bool:
+    """
+    Spread the virus from infected nodes to their neighbors.
+
+    Parameters:
+    ----------
+    graph : nx.DiGraph
+        Directed graph representing the network.
+    infected_nodes : list
+        List of currently infected nodes.
+
+    Returns:
+    -------
+    bool
+        True if there are new infections, False otherwise.
+
+    Examples:
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_nodes_from([(1, {"status": 'infected'}), (2, {"status": 'vulnerable'}), (3, {"status": 'vulnerable'})])
+    >>> G.add_edges_from([(1, 2), (2, 3)])
+    >>> infected_nodes = [1]
+    >>> spread_virus(G, infected_nodes)
+    True
+    >>> G.nodes(data=True)
+    NodeDataView({1: {'status': 'infected'}, 2: {'status': 'infected'}, 3: {'status': 'vulnerable'}})
+    """
+    new_infected_nodes = []
+    for node in infected_nodes:
+        for neighbor in graph.neighbors(node):
+            if graph.nodes[neighbor]['status'] == Status.VULNERABLE.value:
+                graph.nodes[neighbor]['status'] = Status.INFECTED.value
+                new_infected_nodes.append(neighbor)
+                logger.debug("SPREAD VIRUS: Node " + f'{neighbor}' + " has been infected from node " + f'{node}')
+
+    infected_nodes.clear()
+    #display_graph(graph)
+    for node in new_infected_nodes:
+        infected_nodes.append(node)  
+    return bool(infected_nodes)
+
+
+def spread_vaccination(graph:nx.DiGraph, vaccinated_nodes:list) -> None:
+    """
+    Spread the vaccination from vaccinated nodes to their neighbors.
+
+    Parameters:
+    ----------
+    graph : nx.DiGraph
+        Directed graph representing the network.
+    vaccinated_nodes : list
+        List of currently vaccinated nodes.
+
+    Examples:
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_nodes_from([(1, {"status": 'directly_vaccinated'}), (2, {"status": 'vulnerable'}), (3, {"status": 'vulnerable'})])
+    >>> G.add_edges_from([(1, 2), (2, 3)])
+    >>> vaccinated_nodes = [1]
+    >>> spread_vaccination(G, vaccinated_nodes)
+    >>> G.nodes(data=True)
+    NodeDataView({1: {'status': 'directly_vaccinated'}, 2: {'status': 'vaccinated'}, 3: {'status': 'vulnerable'}})
+    """
+    new_vaccinated_nodes = []
+    for node in vaccinated_nodes:
+        for neighbor in graph.neighbors(node):
+            if graph.nodes[neighbor]['status'] == Status.VULNERABLE.value:
+                graph.nodes[neighbor]['status'] = Status.VACCINATED.value
+                new_vaccinated_nodes.append(neighbor)
+                logger.debug("SPREAD VACCINATION: Node " + f'{neighbor}' + " has been vaccinated from node " + f'{node}')
+
+    vaccinated_nodes.clear()
+    #display_graph(graph)
+    for node in new_vaccinated_nodes:
+        vaccinated_nodes.append(node)
+    return
+
+def vaccinate_node(graph:nx.DiGraph, node:int) -> None:
+    """
+    Directly vaccinate a specific node in the graph.
+
+    Parameters:
+    ----------
+    graph : nx.DiGraph
+       Directed graph representing the network.
+    node : int
+        Node to be vaccinated.
+
+    Examples:
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_node(1, status=0)
+    >>> vaccinate_node(G, 1)
+    >>> G.nodes(data=True)
+    NodeDataView({1: {'status': 'directly vaccinated'}})
+    """
+    graph.nodes[node]['status'] = Status.DIRECTLY_VACCINATED.value
+    logger.info("Node " + f'{node}' + " has been directly vaccinated")
+    #display_graph(graph)
+    return
+
+def clean_graph(graph:nx.DiGraph) -> None:
+    """
+    Reset the graph to its base state where all nodes are targets.
+
+    Parameters:
+    ----------
+    graph : nx.DiGraph
+       Directed graph representing the network.
+
+    Examples:
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_nodes_from([(1, {"status": 1}), (2, {"status": 2}), (3, {"status": 0})])
+    >>> clean_graph(G)
+    >>> G.nodes(data=True)
+    NodeDataView({1: {'status': 'vulnerable'}, 2: {'status': 'vulnerable'}, 3: {'status': 'vulnerable'}})
+    """
+    
+    for node in graph.nodes:
+        graph.nodes[node]['status'] = Status.VULNERABLE.value
+    return
+
+# ============================ End Spreading Max-Save ============================
+
+# ===========================  Non-Spreading Min-Budget-Dirlay ============================
+def adjust_nodes_capacity(graph:nx.DiGraph, source:int) -> list:
+    """
+    Adjust the capacity of nodes based on the layer they belong to.
+    The capacity is based on the formula in the article at the DirLayNet algorithm section.
+
+    Parameters:
+    ----------
+    graph : nx.DiGraph
+        Directed graph representing the network.
+    source : int
+        Source node.
+
+    Returns:
+    -------
+    layers: list
+        List of nodes grouped by layers.
+
+    Examples:
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_edges_from([(1, 2), (2, 3), (3, 4)])
+    >>> layers = adjust_nodes_capacity(G, 1)
+    >>> layers
+    [[1], [2], [3], [4]]
+    >>> G.nodes(data=True)
+    NodeDataView({1: {}, 2: {'capacity': 0.5454545454545455}, 3: {'capacity': 0.27272727272727276}, 4: {'capacity': 0.18181818181818182}})
+    """
+    logger.debug(f"Starting to adjust node capacity for dirlay graph nodes...") 
+
+    layers = (list(nx.bfs_layers(graph,source)))
+    harmonic_sum = 0.0
+    for i in range(1,len(layers)):
+        harmonic_sum = harmonic_sum + 1/i
+    for index in range(1,len(layers)):
+        for node in layers[index]:
+            graph.nodes[node]['capacity'] = 1/(index*harmonic_sum)
+            logger.info(f"Added Capacity {1/(index*harmonic_sum)} for node: {node}") 
+
+    logger.info(f"Done with adding capacity for nodes, with Layers: {layers}")       
+
+    return layers
+
+def create_st_graph(graph:nx.DiGraph, targets:list, new_target:str) -> nx.DiGraph:
+    """
+    Create an s-t graph from the original graph for use in connectivity algorithms.
+
+    Parameters:
+    ----------
+    graph : nx.DiGraph
+        Original directed graph.
+    targets : list
+        List of target nodes.
+
+    Returns:
+    -------
+    G : nx.DiGraph
+        s-t graph.
+
+    Examples:
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_edges_from([(1, 2), (2, 3), (3, 4)])
+    >>> targets = [2, 3]
+    >>> G_st = create_st_graph(G, targets, 't')
+    >>> 't' in G_st.nodes
+    True
+    >>> list(G_st.successors(2))
+    [3, 't']
+    >>> list(G_st.successors(3))
+    [4, 't']
+    """
+    logger.info(f"Creating a s-t graph to connect nodes to save") 
+
+    G = copy.deepcopy(graph)
+    G.add_node(new_target, status = Status.VULNERABLE.value)
+    for node in targets:
+        G.add_edge(node, new_target)
+    #display_graph(G)
+
+    logger.info(f"Done creating a s-t graph") 
+    return G
+
+def min_cut_N_groups(min_cut_nodes: set, layers: list) -> dict:
+    """
+    Using the minimum cut group nodes accordingly.
+
+    Parameters:
+    ----------
+    graph : nx.DiGraph
+        Graph after flow reduction.
+    source : int
+        Source node.
+    layers : list
+        List of lists, where each sublist contains nodes belonging to that layer.
+
+    Returns:
+    -------
+    groups : dict
+        Dictionary with layers as keys and lists of nodes in the minimum cut as values.
+
+    Examples:
+    --------
+
+    """
+    
+    logger.info(f"Finding the correct nodes from each layer according to the min-cut nodes") 
+
+    # Initialize the groups dictionary with empty lists for each layer index
+    groups = {i+1: [] for i in range(len(layers)-1)}
+    
+    # Populate the groups dictionary
+    for item in min_cut_nodes:
+        node , suffix = item.split('_')
+        node = int(node)
+        for i, layer_nodes in enumerate(layers):
+            if node in layer_nodes:
+                groups[i].append(node)
+                break
+
+    logger.info(f"Ni groups: {groups}") 
+    return groups
+
+
+def calculate_vaccine_matrix(layers:list, min_cut_nodes_grouped:dict) -> np.matrix: 
+    """
+    Calculate the vaccine matrix based on the calculation in the article at the DirLayNet algorithm section.
+
+    Parameters:
+    ----------
+    layers : list
+        List of nodes grouped by layers.
+    min_cut_nodes_grouped : dict
+        List of nodes in the minimum cut grouped into layers.
+
+    Returns:
+    -------
+    matrix : np.matrix
+        Vaccine matrix.
+
+    Examples:
+    --------
+    
+    """
+    logger.info(f"Calculating the Vaccine Matrix...")
+
+    matrix_length = max(min_cut_nodes_grouped.keys()) 
+    matrix = np.zeros((matrix_length, matrix_length))
+    for j in range(matrix_length):
+        for i in range(j+1):
+                N_j = len(min_cut_nodes_grouped[j+1])
+                value = N_j / (j + 1) 
+                matrix[i][j] = value
+
+    logger.info(f"Vaccination Matrix Before roundups:\n{matrix}")
+    return matrix
+
+def matrix_to_integers_values(matrix: np.matrix) -> np.matrix:
+    """
+    Convert a matrix with fractional entries to an integral matrix such that
+    the row and column sums are either the floor or ceiling of the original sums.
+    The solution is provided with a construction of a flow graph and then applying a max-flow algorithm on it.
+
+    Parameters:
+    ----------
+    matrix : np.matrix
+        The input matrix with fractional entries.
+
+    Returns:
+    -------
+    np.matrix
+        The converted integral matrix.
+
+    Examples:
+    --------
+    
+    """
+    # dimensions of the matrix
+    logger.info(f"Applying max-flow to transfer the Vaccine Matrix for integers...")
+    rows, cols = matrix.shape
+    
+    row_sums = np.array(matrix.sum(axis=1)).flatten()
+    col_sums = np.array(matrix.sum(axis=0)).flatten()
+    
+    # logger.info(f"Row sums: {row_sums}")
+    # logger.info(f"Column sums: {col_sums}")
+    
+    G = nx.DiGraph()
+    
+    # add source and sink nodes
+    source = 's'
+    sink = 't'
+    G.add_node(source)
+    G.add_node(sink)
+    
+    # add nodes for rows and columns
+    row_nodes = ['r{}'.format(i) for i in range(rows)]
+    col_nodes = ['c{}'.format(j) for j in range(cols)]
+    G.add_nodes_from(row_nodes)
+    G.add_nodes_from(col_nodes)
+    
+    # add edges from source to row nodes with capacities as the ceiling of row sums
+    for i in range(rows):
+        G.add_edge(source, row_nodes[i], capacity=np.ceil(row_sums[i]))
+    
+    # add edges from column nodes to sink with capacities as the ceiling of column sums
+    for j in range(cols):
+        G.add_edge(col_nodes[j], sink, capacity=np.ceil(col_sums[j]))
+    
+    # add edges from row nodes to column nodes with capacity 1
+    for i in range(rows):
+        for j in range(cols):
+            G.add_edge(row_nodes[i], col_nodes[j], capacity=1)
+    
+    # computes the maximum flow
+    flow_value, flow_dict = nx.maximum_flow(G, source, sink)
+    
+    # builds the integral matrix
+    integral_matrix = np.zeros_like(matrix, dtype=int)
+    for i in range(rows):
+        for j in range(cols):
+            if flow_dict[row_nodes[i]][col_nodes[j]] > 0:
+                integral_matrix[i, j] = np.ceil(matrix[i, j])
+            else:
+                integral_matrix[i, j] = np.floor(matrix[i, j])
+
+    logger.info(f"Integral and final Matrix:\n{integral_matrix}")
+
+    return np.matrix(integral_matrix)
+
+
+def min_budget_calculation(matrix: np.matrix) -> int:
+    """
+    Calculate the minimum budget from the matrix.
+
+    Parameters:
+    ----------
+    matrix : np.matrix
+        Input matrix.
+
+    Returns:
+    -------
+    min_budget : int
+        Minimum budget.
+
+    Examples:
+    --------
+    >>> matrix = np.matrix([[0.5, 1.5], [1.2, 0.8]])
+    >>> min_budget_calculation(matrix)
+    3
+    """
+    integral_matrix = matrix_to_integers_values(matrix)
+    rows_sum = integral_matrix.sum(axis=1) # we get column sum as we want to -> on time step i, vaccinate Mij nodes from layer j , for all i ≤ j ≤ .
+    min_budget = int(rows_sum.max())
+    logger.info(f"Min budget needed to save the target nodes: {min_budget}")
+    return min_budget
+
+def dirlay_vaccination_strategy(vacc_matrix: np.matrix, ni_groups: dict) -> list:
+    """
+    Determines a feasible vaccination strategy given the vaccine matrix and the nodes from each layer.
+
+    Parameters:
+    ----------
+    vacc_matrix: np.matrix
+        A matrix where rows represent time steps and columns represent layers, 
+        with each element indicating the number of nodes to vaccinate.
+    ni_groups: dict
+        A dict of layers, where each layer contains nodes to be saved.
+
+    Returns:
+    ----------
+    strategy : list
+        A list of tuples where each tuple represents a node to vaccinate and the corresponding time step index.
+    """
+    logger.info("Calculating the strategy")
+
+    num_steps, num_layers = vacc_matrix.shape
+    strategy = []
+    for i in range(num_steps):
+        for j in range(num_layers):
+            num_nodes_to_vaccinate = int(vacc_matrix[i, j])
+
+            logger.debug(f"On time step {i+1} needs to vaccinate: {num_nodes_to_vaccinate} nodes")
+
+            if num_nodes_to_vaccinate > 0:
+                # Extract the nodes to vaccinate
+                selected_nodes = ni_groups[j+1][:num_nodes_to_vaccinate]
+                
+                logger.debug(f"The selected nodes to vaccinate {selected_nodes}")
+
+                # Create tuples (node, i) and add them directly to strategy
+                strategy.extend((node, i+1) for node in selected_nodes)
+    
+    # sort the strategy by time stamp. 
+    strategy.sort(key=lambda x: (x[1], x[0]))
+    return strategy
+
+# ===========================  End Non-Spreading Max-Save ============================
+
+# ===========================  Heuristic Utilities ===================================
+def find_best_neighbor(graph: nx.DiGraph, infected_nodes: list, remaining_targets: list, overall_targets: list) -> tuple[int, set]:
+    """
+    Find the best node from the infected nodes' successors that saves the most new nodes in targets.
+
+    Parameters
+    ----------
+    graph : nx.DiGraph
+        Directed graph.
+    infected_nodes : list
+        List of all infected nodes that threaten to infect additional nodes.
+    remaining_targets : list
+        List of remaining target nodes to be saved.
+    overall_targets : list
+        List of all target nodes.
+
+    Returns
+    -------
+    best_node : int
+        Best node option to vaccinate.
+    nodes_saved : set
+        Set of nodes that would be saved by vaccinating the best node.
+
+    Examples
+    --------
+    Example 1:
+    >>> G = nx.DiGraph()
+    >>> G.add_nodes_from([0, 1, 2, 3, 4], status='vulnerable')
+    >>> G.add_edges_from([(0, 1), (0, 2), (1, 3), (1, 4)])
+    >>> find_best_neighbor(G, [0], [1, 2, 3, 4], [1, 2, 3, 4])
+    (1, {1, 3, 4})
+    """
+    optional_nodes = set()
+    priority_queue = []
+
+    # Go through the infected_nodes list and collect all their neighbors
+    for node in infected_nodes:
+        optional_nodes.update(graph.neighbors(node))
+
+    for node in optional_nodes:
+        is_target = False
+        if graph.nodes[node]['status'] == Status.VULNERABLE.value:
+            # For each node that is target, we will add only its neighbors that are target as well
+            neighbors_list = list(graph.neighbors(node))
+            vulnerable_neighbors = set()
+            for neighbor in neighbors_list:
+                if graph.nodes[neighbor]['status'] == Status.VULNERABLE.value:
+                    vulnerable_neighbors.add(neighbor)
+            if node in overall_targets:
+                is_target = True
+                vulnerable_neighbors.add(node)
+            common_elements = set(vulnerable_neighbors) & set(remaining_targets)
+            logger.info("node " + f'{node}' + " is saving the nodes " + str(common_elements))
+            
+            # Define the priority tuple
+            node_info = (not is_target, -len(common_elements), -len(vulnerable_neighbors), node, common_elements)
+            heapq.heappush(priority_queue, node_info)
+
+    if priority_queue:
+        best_node_info = heapq.heappop(priority_queue)
+        best_node = best_node_info[3]
+        nodes_saved = best_node_info[4]  
+        logger.info("The best node is: " + f'{best_node}' + " and it's saving nodes: " + str(nodes_saved))
+        return best_node, nodes_saved
+
+    return None, []
+
+# ===========================  End Heuristic Utilities ================================
+
+# ===========================  General Utilities ======================================
+def display_graph(graph:nx.DiGraph) -> None:
+    """
+    Display the graph using Matplotlib.
+
+    Parameters
+    ----------
+    graph : nx.DiGraph
+        Directed graph.
+    """
+    pos = nx.shell_layout(graph)
+    colors = [node_colors.get(data.get('status', 'default'), 'default') for node, data in graph.nodes(data=True)]
+    nx.draw(graph, pos, node_color=colors, with_labels=True, font_weight='bold')
+    
+    if nx.get_edge_attributes(graph, 'weight'):
+        edge_labels = nx.get_edge_attributes(graph, 'weight')
+        nx.draw_networkx_edge_labels(graph, pos, edge_labels=edge_labels)
+    plt.show()
+    return
+
+def parse_json_to_networkx(json_data):
+    """
+    Parse JSON data to create Networkx graphs.
+
+    Parameters
+    ----------
+    json_data : dict
+        JSON data containing graph information.
+
+    Returns
+    -------
+    graphs : dict
+        Dictionary of Networkx graphs.
+
+    Raises
+    ------
+    KeyError
+        If 'vertices' or 'edges' is not found or is not a non-empty list.
+    """
+    graphs = {}
+    for graph_type, graph_data in json_data.items():
+        for graph_name, graph_info in graph_data.items():
+            graph_key = f"{graph_type}_{graph_name}"
+            
+            if "vertices" not in graph_info or not isinstance(graph_info["vertices"], list) or not graph_info["vertices"]:
+                logger.critical(f"Error parsing {graph_type}_{graph_name}: 'vertices' must be a non-empty list.")
+                raise KeyError(f"Error parsing {graph_type}_{graph_name}: 'vertices' must be a non-empty list.")
+            
+            if "edges" not in graph_info or not isinstance(graph_info["edges"], list) or not graph_info["edges"]:
+                logger.critical(f"Error parsing {graph_type}_{graph_name}: 'edges' must be a non-empty list.")
+                raise KeyError(f"Error parsing {graph_type}_{graph_name}: 'edges' must be a non-empty list.")
+            
+            vertices = graph_info["vertices"]
+            edges = [(edge[0], edge[1]) for edge in graph_info["edges"]]
+            G = nx.DiGraph()
+            G.add_nodes_from(vertices, status=Status.VULNERABLE.value)
+            G.add_edges_from(edges)
+            graphs[graph_key] = G
+    return graphs
+
+# ===========================  End General Utilities ============================
+
+if __name__ == "__main__":
+    import doctest
+    result = doctest.testmod(verbose=True)
+    logger.info(f"Doctest results: {result}")
\ No newline at end of file
diff --git a/networkz/algorithms/approximation/tests/test_coalition_formation.py b/networkz/algorithms/approximation/tests/test_coalition_formation.py
index cf39fd1..01465aa 100644
--- a/networkz/algorithms/approximation/tests/test_coalition_formation.py
+++ b/networkz/algorithms/approximation/tests/test_coalition_formation.py
@@ -165,4 +165,4 @@ def test_disconnected_components_weighted_graph_with_k_5_returns_correct_partiti
         # Add random weights to the edges
         for u, v in G.edges():
             G[u][v]["weight"] = random.randint(1, 205)
-        assert match_and_merge(G, k=5) == [[1, 2], [3, 4, 5, 6], [7, 8, 9]]
+        assert match_and_merge(G, k=5) == [[1, 2], [3, 4, 5, 6], [7, 8, 9]]
\ No newline at end of file
diff --git a/networkz/algorithms/approximation/tests/test_firefighter_problem/__init__.py b/networkz/algorithms/approximation/tests/test_firefighter_problem/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/networkz/algorithms/approximation/tests/test_firefighter_problem/graphs.json b/networkz/algorithms/approximation/tests/test_firefighter_problem/graphs.json
new file mode 100644
index 0000000..bbeb176
--- /dev/null
+++ b/networkz/algorithms/approximation/tests/test_firefighter_problem/graphs.json
@@ -0,0 +1,334 @@
+{
+    "Dirlay": {
+        "Graph-1": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4,
+                5
+            ],
+            "edges": [
+                [0, 1],
+                [0, 2],
+                [1, 3],
+                [3, 4],
+                [4, 5]
+            ]
+        },
+        "Graph-2": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4
+            ],
+            "edges": [
+                [0, 1],
+                [0, 2],
+                [2, 3],
+                [1, 4]
+            ]
+        },
+        "Graph-3": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4,
+                5,
+                6,
+                7
+            ],
+            "edges": [
+                [0, 1],
+                [0, 2],
+                [0, 3],
+                [3, 4],
+                [1, 5],
+                [5, 6],
+                [4, 7]
+            ]
+        },
+        "Graph-4": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4,
+                5,
+                6,
+                8
+            ],
+            "edges": [
+                [0, 1],
+                [0, 2],
+                [1, 3],
+                [1, 4],
+                [2, 3],
+                [3, 5],
+                [4, 5],
+                [5, 6],
+                [6, 8]
+            ]
+        },
+        "Graph-5": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4,
+                5,
+                6,
+                7,
+                8
+            ],
+            "edges": [
+                [0, 2],
+                [0, 4],
+                [0, 5],
+                [2, 1],
+                [2, 3],
+                [4, 1],
+                [4, 6],
+                [5, 3],
+                [5, 6],
+                [5, 7],
+                [6, 7],
+                [6, 8],
+                [7, 8]
+            ]
+        }
+    },
+    "RegularGraph": {
+        "Graph-1": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4,
+                5,
+                6
+            ],
+            "edges": [
+                [0, 1],
+                [0, 2],
+                [1, 3],
+                [1, 4],
+                [2, 3],
+                [2, 6],
+                [3, 5]
+            ]
+        },
+        "Graph-2": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4,
+                5,
+                6,
+                7
+            ],
+            "edges": [
+                [0, 5],
+                [0, 2],
+                [1, 7],
+                [2, 5],
+                [3, 7],
+                [4, 0],
+                [4, 7],
+                [6, 2],
+                [6, 3],
+                [6, 0],
+                [6, 1],
+                [7, 6],
+                [7, 4],
+                [7, 3],
+                [7, 0]
+            ]
+        },
+        "Graph-3": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4,
+                5
+            ],
+            "edges": [
+                [0, 1],
+                [0, 2],
+                [1, 3],
+                [1, 4],
+                [1, 5],
+                [2, 3],
+                [2, 4],
+                [2, 5],
+                [3, 5],
+                [4, 5]
+            ]
+        },
+        "Graph-4": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4,
+                5,
+                6,
+                7
+            ],
+            "edges": [
+                [0, 1],
+                [0, 6],
+                [1, 2],
+                [1, 5],
+                [1, 6],
+                [2, 3],
+                [3, 4],
+                [5, 2],
+                [5, 3],
+                [5, 4],
+                [6, 5],
+                [7, 6],
+                [7, 1]
+            ]
+        },
+        "Graph-5": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4,
+                5,
+                6,
+                7
+            ],
+            "edges": [
+                [0, 1],
+                [0, 6],
+                [1, 2],
+                [1, 5],
+                [1, 6],
+                [2, 3],
+                [3, 4],
+                [5, 2],
+                [5, 3],
+                [5, 4],
+                [6, 5],
+                [7, 6],
+                [7, 1]
+            ]
+        },
+        "Graph-6": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4,
+                5,
+                6,
+                7,
+                8,
+                9
+            ],
+            "edges": [
+                [1, 2],
+                [2, 1],
+                [2, 3],
+                [2, 8],
+                [3, 7],
+                [3, 9],
+                [3, 0],
+                [4, 1],
+                [4, 7],
+                [6, 3],
+                [7, 0],
+                [7, 6],
+                [8, 1],
+                [9, 5],
+                [9, 2]
+            ]
+        },
+        "Graph-7": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4,
+                5,
+                6
+            ],
+            "edges": [
+                [1, 5],
+                [1, 4],
+                [1, 3],
+                [2, 6],
+                [2, 3],
+                [3, 0],
+                [3, 4],
+                [5, 3],
+                [6, 4]
+            ]
+        },
+        "Graph-8": {
+            "vertices": [
+                0,
+                1,
+                2,
+                3,
+                4,
+                5,
+                6,
+                7,
+                8,
+                9,
+                10,
+                11,
+                12,
+                13,
+                14
+            ],
+            "edges": [
+                [0, 11],
+                [0, 3],
+                [0, 14],
+                [1, 13],
+                [1, 7],
+                [1, 6],
+                [1, 5],
+                [3, 14],
+                [5, 1],
+                [5, 0],
+                [6, 5],
+                [7, 4],
+                [7, 13],
+                [8, 5],
+                [9, 14],
+                [10, 12],
+                [11, 10],
+                [12, 10],
+                [12, 6],
+                [12, 2],
+                [13, 11],
+                [14, 13],
+                [14, 6],
+                [14, 11],
+                [14, 8]
+            ]
+        }
+    }
+}
diff --git a/networkz/algorithms/approximation/tests/test_firefighter_problem/test_heuristic_maxsave.py b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_heuristic_maxsave.py
new file mode 100644
index 0000000..6e79cb2
--- /dev/null
+++ b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_heuristic_maxsave.py
@@ -0,0 +1,177 @@
+"""
+The Paper - 
+Approximability of the Firefighter Problem Computing Cuts over Time
+
+Paper Link -
+https://www.math.uwaterloo.ca/~cswamy/papers/firefighter-journ.pdf
+
+Authors - 
+Elliot Anshelevich
+Deeparnab Chakrabarty
+Ameya Hate 
+Chaitanya Swamy
+
+Developers - 
+Yuval Bubnovsky
+Almog David
+Shaked Levi
+"""
+
+import pytest
+import networkx as nx
+import json
+import random
+import logging
+import os
+import time
+
+from networkz.algorithms.approximation.firefighter_problem.Firefighter_Problem import heuristic_maxsave, spreading_maxsave
+from networkz.algorithms.approximation.firefighter_problem.Utils import parse_json_to_networkx, Status
+
+def setup_logger():
+    logger = logging.getLogger('firefighter_problem_tests')
+    logger.setLevel(logging.INFO)
+    
+    console_handler = logging.StreamHandler()
+    console_handler.setLevel(logging.INFO)
+    
+    formatter = logging.Formatter('%(asctime)s - %(levelname)s - %(message)s')
+    console_handler.setFormatter(formatter)
+    
+    logger.addHandler(console_handler)
+    return logger
+
+logger = setup_logger()
+
+path_to_graphs = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'graphs.json')
+if os.path.exists(path_to_graphs):
+    with open(path_to_graphs, "r") as file:
+        json_data = json.load(file)
+else:
+    raise FileNotFoundError(f"{path_to_graphs} does not exist.")
+graphs = parse_json_to_networkx(json_data)
+
+
+@pytest.mark.parametrize("graph_key, budget, source, targets", [
+    ("RegularGraph_Graph-1", 1, -2, [1, 2, 3, 4, 5, 6]),
+    ("RegularGraph_Graph-4", 1, 8, [1, 2, 4, 6, 7]),
+    ("RegularGraph_Graph-6", 1, 10, [0, 2, 3, 5, 6, 7, 8, 9]),
+    ("RegularGraph_Graph-8", 1, 17, [1, 7, 12, 14, 8, 3, 11, 2]),
+    ("RegularGraph_Graph-3", 1, 6, [1, 3, 5]),
+])
+def test_source_not_in_graph(graph_key, budget, source, targets):
+    with pytest.raises(ValueError):
+        heuristic_maxsave(graphs[graph_key], budget, source, targets)
+
+@pytest.mark.parametrize("graph_key, budget, source, targets", [
+    ("RegularGraph_Graph-2", 1, 0, [1, 2, 3, 9, 5, 16]),
+    ("RegularGraph_Graph-3", 1, 4, [1, 2, 3, 6, 7]),
+    ("RegularGraph_Graph-6", 1, 3, [0, 2, 5, 6, 7, 8, 10]),
+    ("RegularGraph_Graph-8", 1, 11, [1, 3, 12, 19, 8, 10, 4, 2]),
+    ("RegularGraph_Graph-7", 1, 2, [1, 3, -1, 5]),
+])
+def test_target_not_in_graph(graph_key, budget, source, targets):
+    with pytest.raises(ValueError):
+        heuristic_maxsave(graphs[graph_key], budget, source, targets)
+
+@pytest.mark.parametrize("graph_key, budget, source, targets", [
+    ("RegularGraph_Graph-1", 1, 0, [1, 2, 3, 0, 4, 5, 6]),
+    ("RegularGraph_Graph-3", 1, 1, [5, 1, 4]),
+    ("RegularGraph_Graph-4", 1, 4, [1, 2, 3, 4, 5, 6, 7]),
+    ("RegularGraph_Graph-6", 1, 0, [0, 3, 5, 6, 7, 8, 9]),
+    ("RegularGraph_Graph-8", 1, 0, [13, 10, 8, 6, 5, 4, 3, 0, 1, 2]),
+])
+def test_source_is_target(graph_key, budget, source, targets):
+    with pytest.raises(ValueError):
+        heuristic_maxsave(graphs[graph_key], budget, source, targets)
+
+@pytest.mark.parametrize("graph_key, budget, source, targets, expected_length", [
+    ("RegularGraph_Graph-1", 1, 0, [1, 2, 3, 4, 5, 6], 2),
+    ("Dirlay_Graph-5", 2, 0, [1, 2, 3, 4, 5, 6, 7, 8], 3),
+])
+def test_strategy_length(graph_key, budget, source, targets, expected_length):
+    logger.info(f"Testing strategy length for {graph_key}")
+    graph = graphs[graph_key]
+    calculated_strategy = spreading_maxsave(graph, budget, source, targets)[0]
+    logger.info(f"Calculated strategy: {calculated_strategy}")
+    
+    assert len(calculated_strategy) == expected_length
+    logger.info(f"Strategy length test passed for {graph_key}")
+
+@pytest.mark.parametrize("graph_key, budget, source, targets, expected_strategy", [
+    ("RegularGraph_Graph-1", 1, 0, [1, 2, 3, 4, 5, 6], [(1, 1), (6, 2)]),
+    ("Dirlay_Graph-5", 2, 0, [1, 2, 3, 4, 5, 6, 7, 8], [(5, 1), (2, 1)]),
+])
+def test_save_all_vertices(graph_key, budget, source, targets, expected_strategy):
+    logger.info(f"Testing save all vertices for {graph_key}")
+    graph = graphs[graph_key]
+    calculated_strategy = heuristic_maxsave(graph, budget, source, targets)[0]
+    logger.info(f"Calculated strategy: {calculated_strategy}")
+    
+    assert calculated_strategy == expected_strategy
+    logger.info(f"Save all vertices test passed for {graph_key}")
+
+@pytest.mark.parametrize("graph_key, budget, source, targets, expected_save_amount", [
+    ("RegularGraph_Graph-6", 2, 1, [3, 9, 0, 5, 6], 5),
+    ("RegularGraph_Graph-4", 1, 0, [2, 6, 4], 3),
+])
+def test_save_subgroup_vertices(graph_key, budget, source, targets, expected_save_amount):
+    logger.info(f"Testing save subgroup vertices for {graph_key}")
+    graph = graphs[graph_key]
+    calculated_strategy = len(heuristic_maxsave(graph, budget, source, targets)[1])
+    logger.info(f"Calculated strategy: {calculated_strategy}")
+    
+    assert calculated_strategy >= expected_save_amount
+    logger.info(f"Save subgroup vertices test passed for {graph_key}")
+    
+
+def test_random_graph_comparison():
+    logger.info("Starting test_random_graph_comparison:")
+    try:
+        for i in range(2):
+            num_nodes = random.randint(5, 50)
+            nodes = list(range(num_nodes + 1))
+            num_edges = 100
+            save_amount = random.randint(5, num_nodes)
+            targets = []
+            G = nx.DiGraph()
+            
+            G.add_nodes_from(nodes, status=Status.VULNERABLE.value)
+            for _ in range(num_edges):
+                source = random.randint(0, num_nodes - 1)
+                target = random.randint(0, num_nodes - 1)
+                if source != target:  # Ensure no self-loops
+                    G.add_edge(source, target)
+            for node in range(save_amount):
+                probability = random.random()
+                if probability < 0.9 and node != 0:
+                    targets.append(node)
+            
+            logger.info(f"Random Graph {i+1} - Targets: {targets}")
+            
+            start_time = time.time()
+            spreading = spreading_maxsave(G, 1, 0, targets)
+            spreading_answer = spreading_maxsave(G, 1, 0, targets)[1]
+            spreading_time = time.time() - start_time
+            
+            start_time = time.time()
+            heuristic = heuristic_maxsave(G, 1, 0, targets)
+            heuristic_answer = heuristic_maxsave(G, 1, 0, targets)[1]
+
+            heuristic_time = time.time() - start_time
+            
+            logger.info(f"Random Graph {i+1} - Spreading Result: {spreading}, Heuristic Result: {heuristic}")
+            logger.info(f"Random Graph {i+1} - Spreading Time: {spreading_time:.6f}s, Heuristic Time: {heuristic_time:.6f}s")
+            
+            if len(spreading_answer) > len(heuristic_answer):
+                warning_message = f"Warning: Heuristic result ({len(heuristic_answer)}) is less than spreading result ({len(spreading_answer)}) for Random Graph {i+1}"
+                logger.warning(warning_message)
+
+    finally:
+        logger.info("Finished test_random_graph_comparison.")
+        logger.info("-" * 100)
+
+
+if __name__ == "__main__":
+     pytest.main(["-v",__file__])
+
diff --git a/networkz/algorithms/approximation/tests/test_firefighter_problem/test_heuristic_minbudget.py b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_heuristic_minbudget.py
new file mode 100644
index 0000000..353f27e
--- /dev/null
+++ b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_heuristic_minbudget.py
@@ -0,0 +1,144 @@
+"""
+
+The Paper - 
+Approximability of the Firefighter Problem Computing Cuts over Time
+
+Paper Link -
+https://www.math.uwaterloo.ca/~cswamy/papers/firefighter-journ.pdf
+
+Authors - 
+Elliot Anshelevich
+Deeparnab Chakrabarty
+Ameya Hate 
+Chaitanya Swamy
+
+Developers - 
+Yuval Bubnovsky
+Almog David
+Shaked Levi
+
+"""
+import pytest
+import random
+import time
+import logging
+import os
+import json
+
+from networkz.algorithms.approximation.firefighter_problem.Firefighter_Problem import spreading_minbudget, heuristic_minbudget
+from networkz.algorithms.approximation.firefighter_problem.Random_Graph_Generator import generate_random_DiGraph
+from networkz.algorithms.approximation.firefighter_problem.Utils import parse_json_to_networkx
+
+
+def setup_logger():
+    logger = logging.getLogger('firefighter_problem_tests')
+    logger.setLevel(logging.INFO)
+    
+    console_handler = logging.StreamHandler()
+    console_handler.setLevel(logging.INFO)
+    
+    formatter = logging.Formatter('%(asctime)s - %(levelname)s - %(message)s')
+    console_handler.setFormatter(formatter)
+    
+    logger.addHandler(console_handler)
+    return logger
+
+logger = setup_logger()
+
+
+@pytest.fixture
+def sample_json_data():
+    return {
+        "Dirlay": {
+            "Graph-1": {
+                "vertices": [0, 1, 2, 3, 4, 5],
+                "edges": [[0, 1], [0, 2]]
+            },
+        },
+        "RegularGraph": {
+            "Graph-1": {
+                "vertices": [0, 1, 2],
+                "edges": [[0, 1], [1, 2]]
+            },
+        }
+    }
+
+def get_graphs():
+    path_to_graphs = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'graphs.json')
+    if os.path.exists(path_to_graphs):
+        with open(path_to_graphs, "r") as file:
+            json_data = json.load(file)
+    else:
+        raise FileNotFoundError(f"{path_to_graphs} does not exist.")
+    
+    graphs = parse_json_to_networkx(json_data)
+    return graphs
+
+graphs = get_graphs()
+
+@pytest.mark.parametrize("G, source, targets, directed", [
+    (graphs["RegularGraph_Graph-1"], -3, [1, 0, 4, 5, 2, 6], True),
+    (graphs["RegularGraph_Graph-4"], 10, [1, 3, 5, 6, 7], False),
+    (graphs["RegularGraph_Graph-6"], 12, [9, 2, 3, 4, 6, 7], True),
+    (graphs["RegularGraph_Graph-8"], -1, [7, 10, 4, 9, 3, 11, 2], False),
+    (graphs["RegularGraph_Graph-3"], 8, [1, 4, 2], True)
+])
+def test_source_not_in_graph(G, source, targets, directed):
+    with pytest.raises(ValueError, match="Error: The source node isn't on the graph"):
+        heuristic_minbudget(G, source, targets, directed)
+
+@pytest.mark.parametrize("G, source, targets, directed", [
+    (graphs["RegularGraph_Graph-2"], 2, [0, 4, 5, 11, 6], True),
+    (graphs["RegularGraph_Graph-3"], 3, [0, 4, 5, -1, 1, 2], False),
+    (graphs["RegularGraph_Graph-6"], 7, [9, 2, 4, 5, 8, 11], True),
+    (graphs["RegularGraph_Graph-8"], 10, [0, 2, 4, 5, 8, 11, 12, 3, 15], False),
+    (graphs["RegularGraph_Graph-7"], 1, [3, 5, 4, 0, 13], True)
+])
+def test_target_not_in_graph(G, source, targets, directed):
+    with pytest.raises(ValueError, match="Error: Not all nodes in the targets list are on the graph."):
+        heuristic_minbudget(G, source, targets, directed)
+
+@pytest.mark.parametrize("G, source, targets, directed", [
+    (graphs["RegularGraph_Graph-1"], 0, [1, 2, 3, 0, 4, 5, 6], True),
+    (graphs["RegularGraph_Graph-3"], 1, [5, 1, 4], False),
+    (graphs["RegularGraph_Graph-4"], 4, [1, 2, 3, 4, 5, 6, 7], True),
+    (graphs["RegularGraph_Graph-6"], 0, [0, 3, 5, 6, 7, 8, 9], False),
+    (graphs["RegularGraph_Graph-8"], 0, [13, 10, 8, 6, 5, 4, 3, 0, 1, 2], True)
+])
+def test_source_is_target(G, source, targets, directed):
+    with pytest.raises(ValueError, match="Error: The source node can't be a part of the targets list, since the virus is spreading from the source"):
+        heuristic_minbudget(G, source, targets, directed)
+
+
+@pytest.mark.parametrize("i", range(10))
+def test_random_graph_comparison(i):
+    logger.info(f"Starting test_random_graph_comparison for Random Graph {i+1}:")
+    try:
+        G =  generate_random_DiGraph(num_nodes=100, edge_probability=0.5)
+
+        num_targets = random.randint(1, int(len(G.nodes) / 2) + 1)
+        nodes_to_sample = list(G.nodes)
+        nodes_to_sample.remove(0)
+        targets = random.sample(list(nodes_to_sample), num_targets)
+
+        start_time = time.time()
+        spreading_answer = spreading_minbudget(G, 0, targets)[0]
+        spreading_time = time.time() - start_time
+
+        start_time = time.time()
+        heuristic_answer = heuristic_minbudget(G, 0, targets, True)[0]
+        heuristic_time = time.time() - start_time
+
+        logger.info(f"Random Graph {i+1} - Spreading Result: {spreading_answer}, Heuristic Result: {heuristic_answer}")
+        logger.info(f"Random Graph {i+1} - Spreading Time: {spreading_time:.6f}s, Heuristic Time: {heuristic_time:.6f}s")
+
+        if heuristic_answer > spreading_answer:
+            warning_message = f"Warning: Heuristic result ({heuristic_answer}) is greater than spreading result ({spreading_answer}) for Random Graph {i+1}"
+            logger.warning(warning_message)
+
+    finally:
+        logger.info(f"Finished test_random_graph_comparison for Random Graph {i+1}.")
+        logger.info("-" * 100)
+
+if __name__ == "__main__":
+    pytest.main(["-v", __file__])
\ No newline at end of file
diff --git a/networkz/algorithms/approximation/tests/test_firefighter_problem/test_non_spreading_dirlaynet_minbudget.py b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_non_spreading_dirlaynet_minbudget.py
new file mode 100644
index 0000000..15a2347
--- /dev/null
+++ b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_non_spreading_dirlaynet_minbudget.py
@@ -0,0 +1,385 @@
+"""
+
+The Paper - 
+Approximability of the Firefighter Problem Computing Cuts over Time
+
+Paper Link -
+https://www.math.uwaterloo.ca/~cswamy/papers/firefighter-journ.pdf
+
+Authors - 
+Elliot Anshelevich
+Deeparnab Chakrabarty
+Ameya Hate 
+Chaitanya Swamy
+
+Developers - 
+Yuval Bubnovsky
+Almog David
+Shaked Levi
+
+"""
+
+import pytest
+import json
+import numpy as np
+import math
+import random
+import os
+
+from networkz.algorithms.approximation.firefighter_problem.Firefighter_Problem import non_spreading_dirlaynet_minbudget
+from networkz.algorithms.approximation.firefighter_problem.Utils import adjust_nodes_capacity
+from networkz.algorithms.approximation.firefighter_problem.Utils import create_st_graph
+from networkz.algorithms.approximation.firefighter_problem.Utils import parse_json_to_networkx
+from networkz.algorithms.max_flow_with_node_capacity import min_cut_with_node_capacity
+from networkz.algorithms.approximation.firefighter_problem.Utils import calculate_vaccine_matrix
+from networkz.algorithms.approximation.firefighter_problem.Utils import min_cut_N_groups
+from networkz.algorithms.approximation.firefighter_problem.Utils import matrix_to_integers_values
+from networkz.algorithms.approximation.firefighter_problem.Utils import min_budget_calculation
+from networkz.algorithms.approximation.firefighter_problem.Random_Graph_Generator import generate_random_layered_network
+
+path_to_graphs = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'graphs.json')
+if os.path.exists(path_to_graphs):
+    with open(path_to_graphs, "r") as file:
+        json_data = json.load(file)
+else:
+    raise FileNotFoundError(f"{path_to_graphs} does not exist.")
+
+graphs = parse_json_to_networkx(json_data)
+
+@pytest.mark.parametrize("graph_key, source, targets", [
+    ("Dirlay_Graph-1", -3, [0, 5]),
+    ("Dirlay_Graph-2", 13, [0, 1, 4]),
+    ("Dirlay_Graph-3", 15, [0, 6, 7]),
+    ("Dirlay_Graph-4", -1, [1, 3, 5, 7]),
+])
+def test_source_not_in_graph(graph_key, source, targets):
+    with pytest.raises(ValueError):
+        non_spreading_dirlaynet_minbudget(graphs[graph_key], source, targets)
+
+@pytest.mark.parametrize("graph_key, source, targets", [
+    ("Dirlay_Graph-1", 0, [1, 5, 7]),
+    ("Dirlay_Graph-2", 1, [0, 2, -1, 9]),
+    ("Dirlay_Graph-3", 4, [0, 1, 2, 11, 12, 13, 14]),
+    ("Dirlay_Graph-4", 0, [1, 3, 5, 7, 15, 20]),
+])
+def test_target_not_in_graph(graph_key, source, targets):
+    with pytest.raises(ValueError):
+        non_spreading_dirlaynet_minbudget(graphs[graph_key], source, targets)
+
+@pytest.mark.parametrize("graph_key, source, targets", [
+    ("Dirlay_Graph-1", 0, [0, 5]),
+    ("Dirlay_Graph-2", 1, [0, 1, 4]),
+    ("Dirlay_Graph-3", 6, [0, 6, 7]),
+    ("Dirlay_Graph-4", 3, [1, 3, 5, 7]),
+])
+def test_source_is_target(graph_key, source, targets):
+    with pytest.raises(ValueError):
+        non_spreading_dirlaynet_minbudget(graphs[graph_key], source, targets)
+
+    
+# Test 1
+# graph building
+graph_1 = graphs["Dirlay_Graph-1"]
+layers_1 = adjust_nodes_capacity(graph_1, 0) # src is 0 
+targets_1 = [1, 2, 3]  # saving 1,2,3
+G1 = create_st_graph(graph_1, targets_1,'t')
+reduction_G1_min_cut = min_cut_with_node_capacity(G1, 0)
+N_1_groups = min_cut_N_groups(reduction_G1_min_cut,layers_1)
+matrix_1 = calculate_vaccine_matrix(layers_1, N_1_groups)
+integer_matrix_1 = matrix_to_integers_values(matrix_1) 
+min_budget_1 = min_budget_calculation(integer_matrix_1)
+
+# Test 2
+# graph building
+graph_2 = graphs["Dirlay_Graph-2"]
+layers_2 = adjust_nodes_capacity(graph_2, 0)  # src is 0
+targets_2 = [2, 4]  # saving 2,4
+G2 = create_st_graph(graph_2, targets_2,'t')
+reduction_G2_min_cut = min_cut_with_node_capacity(G2, 0) 
+N_2_groups = min_cut_N_groups(reduction_G2_min_cut, layers_2)
+matrix_2 = calculate_vaccine_matrix(layers_2, N_2_groups)
+integer_matrix_2 = matrix_to_integers_values(matrix_2)
+min_budget_2 = min_budget_calculation(integer_matrix_2)
+
+# Test 3
+# graph building
+graph_3 = graphs["Dirlay_Graph-3"]
+layers_3 = adjust_nodes_capacity(graph_3, 0)  # src is 0
+targets_3 = [1, 5, 7]  # saving 1,5,7
+G3 = create_st_graph(graph_3, targets_3,'t')
+reduction_G3_min_cut = min_cut_with_node_capacity(G3, 0)
+N_3_groups = min_cut_N_groups(reduction_G3_min_cut, layers_3)
+matrix_3 = calculate_vaccine_matrix(layers_3, N_3_groups)
+integer_matrix_3 = matrix_to_integers_values(matrix_3)
+min_budget_3 = min_budget_calculation(integer_matrix_3)
+
+# Test 4
+# graph building
+graph_4 = graphs["Dirlay_Graph-4"]
+layers_4 = adjust_nodes_capacity(graph_4, 0)  # src is 0
+targets_4 = [4, 5, 6, 8]  # saving 4,5,6,8
+G4 = create_st_graph(graph_4, targets_4,'t')
+reduction_G4_min_cut = min_cut_with_node_capacity(G4, 0)
+N_4_groups = min_cut_N_groups(reduction_G4_min_cut, layers_4)
+matrix_4 = calculate_vaccine_matrix(layers_4, N_4_groups)
+integer_matrix_4 = matrix_to_integers_values(matrix_4)
+min_budget_4 = min_budget_calculation(integer_matrix_4)
+
+def test_adjust_nodes_capacity():
+    """
+    This test checks if the node capacity and layers are correct.
+    """
+    # Tolerance for floating point comparisons, this is simply to not inturrpt in the after point shenanings.
+    tolerance = 1e-6
+
+    # Test 1
+    layers_1_check = [[0], [1, 2], [3], [4], [5]]
+    assert adjust_nodes_capacity(graph_1, 0) == layers_1_check
+    assert math.isclose(graph_1.nodes[1]['capacity'], 1 / (1 * (1/1 + 1/2 + 1/3 + 1/4)), rel_tol=tolerance)
+    assert math.isclose(graph_1.nodes[2]['capacity'], 1 / (1 * (1/1 + 1/2 + 1/3 + 1/4)), rel_tol=tolerance)
+    assert math.isclose(graph_1.nodes[3]['capacity'], 1 / (2 * (1/1 + 1/2 + 1/3 + 1/4)), rel_tol=tolerance)
+    assert math.isclose(graph_1.nodes[4]['capacity'], 1 / (3 * (1/1 + 1/2 + 1/3 + 1/4)), rel_tol=tolerance)
+    assert math.isclose(graph_1.nodes[5]['capacity'], 1 / (4 * (1/1 + 1/2 + 1/3 + 1/4)), rel_tol=tolerance)
+
+    # Test 2
+    layers_2_check = [[0], [1, 2], [4, 3]]
+    assert adjust_nodes_capacity(graph_2, 0) == layers_2_check
+    assert math.isclose(graph_2.nodes[1]['capacity'], 1 / (1 * (1/1 + 1/2)), rel_tol=tolerance)
+    assert math.isclose(graph_2.nodes[2]['capacity'], 1 / (1 * (1/1 + 1/2)), rel_tol=tolerance)
+    assert math.isclose(graph_2.nodes[3]['capacity'], 1 / (2 * (1/1 + 1/2)), rel_tol=tolerance)
+    assert math.isclose(graph_2.nodes[4]['capacity'], 1 / (2 * (1/1 + 1/2)), rel_tol=tolerance)
+
+    # Test 3
+    layers_3_check = [[0], [1, 2, 3], [5, 4], [6, 7]]
+    assert adjust_nodes_capacity(graph_3, 0) == layers_3_check
+    assert math.isclose(graph_3.nodes[1]['capacity'], 1 / (1 * (1/1 + 1/2 + 1/3)), rel_tol=tolerance)
+    assert math.isclose(graph_3.nodes[2]['capacity'], 1 / (1 * (1/1 + 1/2 + 1/3)), rel_tol=tolerance)
+    assert math.isclose(graph_3.nodes[3]['capacity'], 1 / (1 * (1/1 + 1/2 + 1/3)), rel_tol=tolerance)
+    assert math.isclose(graph_3.nodes[4]['capacity'], 1 / (2 * (1/1 + 1/2 + 1/3)), rel_tol=tolerance)
+    assert math.isclose(graph_3.nodes[5]['capacity'], 1 / (2 * (1/1 + 1/2 + 1/3)), rel_tol=tolerance)
+    assert math.isclose(graph_3.nodes[6]['capacity'], 1 / (3 * (1/1 + 1/2 + 1/3)), rel_tol=tolerance)
+    assert math.isclose(graph_3.nodes[7]['capacity'], 1 / (3 * (1/1 + 1/2 + 1/3)), rel_tol=tolerance)
+
+    # Test 4
+    layers_4_check = [[0], [1, 2], [3, 4], [5], [6], [8]]
+    assert adjust_nodes_capacity(graph_4, 0) == layers_4_check
+    assert math.isclose(graph_4.nodes[1]['capacity'], 1 / (1 * (1/1 + 1/2 + 1/3 + 1/4 + 1/5)), rel_tol=tolerance)
+    assert math.isclose(graph_4.nodes[2]['capacity'], 1 / (1 * (1/1 + 1/2 + 1/3 + 1/4 + 1/5)), rel_tol=tolerance)
+    assert math.isclose(graph_4.nodes[3]['capacity'], 1 / (2 * (1/1 + 1/2 + 1/3 + 1/4 + 1/5)), rel_tol=tolerance)
+    assert math.isclose(graph_4.nodes[4]['capacity'], 1 / (2 * (1/1 + 1/2 + 1/3 + 1/4 + 1/5)), rel_tol=tolerance)
+    assert math.isclose(graph_4.nodes[5]['capacity'], 1 / (3 * (1/1 + 1/2 + 1/3 + 1/4 + 1/5)), rel_tol=tolerance)
+    assert math.isclose(graph_4.nodes[6]['capacity'], 1 / (4 * (1/1 + 1/2 + 1/3 + 1/4 + 1/5)), rel_tol=tolerance)
+    assert math.isclose(graph_4.nodes[8]['capacity'], 1 / (5 * (1/1 + 1/2 + 1/3 + 1/4 + 1/5)), rel_tol=tolerance)
+
+
+
+def test_create_st_graph() : 
+    """
+    Creates the s-t graph and connects the nodes we want to save.
+    """
+    # Test1
+    # edges check
+    assert "t" in G1
+    assert G1.has_edge(1, "t")
+    assert G1.has_edge(2, "t")
+    assert G1.has_edge(3, "t")
+
+    # Test2
+    # edges check
+    assert "t" in G2
+    assert G2.has_edge(2, "t")
+    assert G2.has_edge(4, "t")
+
+    # Test3
+    # edges check
+    assert "t" in G3
+    assert G3.has_edge(1, "t")
+    assert G3.has_edge(5, "t")
+    assert G3.has_edge(7, "t")
+
+    # Test4
+    # edges check
+    assert "t" in G4
+    assert G4.has_edge(4, "t")
+    assert G4.has_edge(5, "t")
+    assert G4.has_edge(6, "t")
+    assert G4.has_edge(8, "t")
+
+def test_min_cut_N_groups(): 
+    """
+    This test validates the nodes taken from the min-cut create the right groups (N_1...N_l).
+    """
+    def sort_dict_values(d): #| this is for sorting purposes , cases where [1,2] or [2,1] it does not really matters as we need to vaccinate them.
+        return {k: sorted(v) for k, v in d.items()}
+
+    # Test 1 
+    # checking equality
+    N1_groups_check = {1: [1, 2], 2: [], 3: [], 4: []}
+    result_1 = min_cut_N_groups(reduction_G1_min_cut, layers_1)
+    assert sort_dict_values(result_1) == sort_dict_values(N1_groups_check)
+
+    # Test 2
+    # checking equality
+    N2_groups_check = {1: [2], 2: [4]}
+    result_2 = min_cut_N_groups(reduction_G2_min_cut, layers_2)
+    assert sort_dict_values(result_2) == sort_dict_values(N2_groups_check)
+
+    # Test 3
+    # checking equality
+    N3_groups_check = {1: [1], 2: [], 3: [7]}
+    result_3 = min_cut_N_groups(reduction_G3_min_cut, layers_3)
+    assert sort_dict_values(result_3) == sort_dict_values(N3_groups_check)
+
+    # Test 4
+    # checking equality
+    N4_groups_check = {1: [], 2: [4], 3: [5], 4: [], 5: []}
+    result_4 = min_cut_N_groups(reduction_G4_min_cut, layers_4)
+    assert sort_dict_values(result_4) == sort_dict_values(N4_groups_check)
+    
+def test_calculate_vaccine_matrix():
+    """
+    This test checks that the calculations made to create the triangular matrix from the min-cut nodes are correct.
+    A matrix is valid if, for any column j, the column sum is exactly |Nj|.
+    """
+    # Test 1
+    # checking equality
+    matrix_1_check = np.array([[2, 0, 0, 0],
+                               [0, 0, 0, 0],
+                               [0, 0, 0, 0],
+                               [0, 0, 0, 0]])
+    np.testing.assert_array_equal(calculate_vaccine_matrix(layers_1, N_1_groups), matrix_1_check)
+
+    # Test 2
+    
+    """
+    Applying the formula: Mij ': =  Nj j , 1≤i≤j≤2 (l=2)
+    N2_groups_check = {1: [2], 2: [4]} 
+    N1 : = {2} |N1| = 1
+    N2 : = {4} |N2| = 1
+
+    1. M11 : i = 1, j = 1
+    |N1|/1 = 1/1 = 1
+    2. M12 : i = 1, j = 2
+    |N2|/2 = 1/2
+    3. M22 : i = 2, j = 2
+    |N2|/2 = 1/2 
+    """
+
+    # checking equality
+    matrix_2_check = np.array([[1, 0.5],
+                               [0, 0.5]])
+    np.testing.assert_array_equal(calculate_vaccine_matrix(layers_2, N_2_groups), matrix_2_check)
+
+    # Test 3
+    """
+    Applying the formula: Mij ': =  Nj j , 1≤i≤j≤2 (l=2)
+    N3_groups_check = {1: [1], 2: [], 3: [7]}
+    N1 : = {1} |N1| = 1
+    N2 : = {0} |N2| = 0
+    N3 := {7} |N3| = 1
+
+    1. M11 : i = 1, j = 1
+    |N1|/1 = 1/1 = 1
+    2. M12 : i = 1, j = 2
+    |N2|/2 = 0/2 = 0
+    3. M13 : i = 1, j = 3
+    |N3|/3 = 1/3 
+    4. M22 : i = 2, j = 2
+    |N2|/2 = 0/2 = 0
+    5. M23 : i = 2 j = 3
+    |N3|/3 = 1/3 
+    5. M33 : i = 2 j = 3
+    |N3|/3 = 1/3 
+    """
+    # checking equality
+    matrix_3_check = np.array([[1, 0, 1/3],
+                               [0, 0, 1/3],
+                               [0, 0, 1/3]])
+    np.testing.assert_array_equal(calculate_vaccine_matrix(layers_3, N_3_groups), matrix_3_check)
+
+    # Test 4
+    # checking equality
+    matrix_4_check = np.array([[0, 0.5, 1/3, 0, 0],
+                               [0, 0.5, 1/3, 0, 0],
+                               [0, 0, 1/3, 0, 0],
+                               [0, 0, 0, 0, 0],
+                               [0, 0, 0, 0, 0]])
+    np.testing.assert_array_equal(calculate_vaccine_matrix(layers_4, N_4_groups), matrix_4_check)
+    
+def test_matrix_to_integers_values(): 
+    """
+    Test the matrix to integers values function.
+    """
+    # Test 1
+    # checking equality
+    matrix_1_check = np.array([[2, 0, 0, 0],
+                               [0, 0, 0, 0],
+                               [0, 0, 0, 0],
+                               [0, 0, 0, 0]])
+    
+    expected_matrix_1 = np.array([[2, 0, 0, 0],
+                                [0, 0, 0, 0],
+                                [0, 0, 0, 0],
+                                [0, 0, 0, 0]])
+    np.testing.assert_array_equal(matrix_to_integers_values(matrix_1_check), expected_matrix_1)
+
+    # Test 2
+    # checking equality
+    matrix_2_check = np.array([[1, 0.5],
+                               [0, 0.5]])
+    
+    expected_matrix_2 = np.array([[1, 1],
+                               [0, 0]])
+    np.testing.assert_array_equal(matrix_to_integers_values(matrix_2_check), expected_matrix_2)
+
+    # Test 3
+    # checking equality
+    matrix_3_check = np.array([[1, 0, 1/3],
+                               [0, 0, 1/3],
+                               [0, 0, 1/3]])
+    
+    expected_matrix_3 = np.array([[1, 0, 1],
+                               [0, 0, 0],
+                               [0, 0, 0]])
+    np.testing.assert_array_equal(matrix_to_integers_values(matrix_3_check), expected_matrix_3)
+
+
+def test_min_budget_calculation():
+    """
+    This test validates that the minimum budget is accurate.
+    """
+    # Test 1
+    # checking equality
+    matrix_1_check = np.array([[2, 0, 0, 0],
+                               [0, 0, 0, 0],
+                               [0, 0, 0, 0],
+                               [0, 0, 0, 0]])
+    assert min_budget_calculation(matrix_1_check) == 2
+
+    # Test 2
+    # checking equality
+    matrix_2_check = np.array([[1, 1], #on time i = 1, vaccinate M11(1) nodes from layer 1. , on time i = 2, vaccinante M12(1) nodes from layer 2
+                               [0, 0]])
+    assert min_budget_calculation(matrix_2_check) == 2
+
+    # Test 3
+    # checking equality
+    matrix_3_check = np.array([[1, 0, 1],
+                               [0, 0, 0],
+                               [0, 0, 0]])
+    assert min_budget_calculation(matrix_3_check) == 2
+
+
+def test_non_spreading_dirlaynet_minbudget():
+    G = generate_random_layered_network()
+    source = 0 
+
+    nodes = list(G.nodes())
+    num_targets = random.randint(1, len(nodes) - 1)  # Ensure at least one target node
+    targets = random.sample(nodes[1:], num_targets)  # Randomly choose nodes to save, excluding the source node
+    
+    min_budget = non_spreading_dirlaynet_minbudget(G, source, targets)[0]
+    assert min_budget > 0, "Minimum budget should be non-negative"
+
+if __name__ == "__main__":
+    pytest.main(["-v", __file__])
diff --git a/networkz/algorithms/approximation/tests/test_firefighter_problem/test_non_spreading_minbudget.py b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_non_spreading_minbudget.py
new file mode 100644
index 0000000..16c230a
--- /dev/null
+++ b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_non_spreading_minbudget.py
@@ -0,0 +1,129 @@
+"""
+
+The Paper - 
+Approximability of the Firefighter Problem Computing Cuts over Time
+
+Paper Link -
+https://www.math.uwaterloo.ca/~cswamy/papers/firefighter-journ.pdf
+
+Authors - 
+Elliot Anshelevich
+Deeparnab Chakrabarty
+Ameya Hate 
+Chaitanya Swamy
+
+Developers - 
+Yuval Bubnovsky
+Almog David
+Shaked Levi
+
+"""
+
+import pytest
+import json
+import os
+
+from networkz.algorithms.approximation.firefighter_problem.Firefighter_Problem import non_spreading_minbudget
+from networkz.algorithms.approximation.firefighter_problem.Utils import parse_json_to_networkx
+
+@pytest.fixture
+def sample_json_data():
+    return {
+        "Dirlay": {
+            "Graph-1": {
+                "vertices": [0, 1, 2, 3, 4, 5],
+                "edges": [[0, 1], [0, 2]]
+            },
+        },
+        "RegularGraph": {
+            "Graph-1": {
+                "vertices": [0, 1, 2],
+                "edges": [[0, 1], [1, 2]]
+            },
+        }
+    }
+
+def get_graphs():
+    path_to_graphs = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'graphs.json')
+    if os.path.exists(path_to_graphs):
+        with open(path_to_graphs, "r") as file:
+            json_data = json.load(file)
+    else:
+        raise FileNotFoundError(f"{path_to_graphs} does not exist.")
+    
+    graphs = parse_json_to_networkx(json_data)
+    return graphs
+
+graphs =  get_graphs()
+
+def test_source_not_in_graph():
+    with pytest.raises(ValueError, match="Error: The source node isn't on the graph"):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-1"], -2, [1,2,3,4,5,6])
+
+    with pytest.raises(ValueError, match="Error: The source node isn't on the graph"):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-4"], 8, [1,2,4,6,7])
+
+    with pytest.raises(ValueError, match="Error: The source node isn't on the graph"):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-6"], 10, [0,2,3,5,6,7,8,9])
+
+    with pytest.raises(ValueError, match="Error: The source node isn't on the graph"):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-8"], 17, [1,7,12,14,8,3,11,2])
+
+    with pytest.raises(ValueError, match="Error: The source node isn't on the graph"):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-3"], 6, [1,3,5])
+        
+
+def test_target_not_in_graph():
+    with pytest.raises(ValueError, match="Error: Not all nodes in the targets list are on the graph."):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-2"], 0, [1,2,3,9,5,16])
+
+    with pytest.raises(ValueError, match="Error: Not all nodes in the targets list are on the graph."):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-3"], 4, [1,2,3,6,7])
+
+    with pytest.raises(ValueError, match="Error: Not all nodes in the targets list are on the graph."):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-6"], 3, [0,2,5,6,7,8,10])
+
+    with pytest.raises(ValueError, match="Error: Not all nodes in the targets list are on the graph."):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-8"], 11, [1,3,12,19,8,10,4,2])
+
+    with pytest.raises(ValueError, match="Error: Not all nodes in the targets list are on the graph."):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-7"], 2, [1,3,-1,5])
+        
+
+def test_source_is_target():
+    with pytest.raises(ValueError, match="Error: The source node can't be a part of the targets list, since the virus is spreading from the source"):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-1"], 0, [1,2,3,0,4,5,6])
+    
+    with pytest.raises(ValueError, match="Error: The source node can't be a part of the targets list, since the virus is spreading from the source"):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-3"], 1, [5,1,4])
+    
+    with pytest.raises(ValueError, match="Error: The source node can't be a part of the targets list, since the virus is spreading from the source"):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-4"], 4, [1,2,3,4,5,6,7])
+    
+    with pytest.raises(ValueError, match="Error: The source node can't be a part of the targets list, since the virus is spreading from the source"):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-6"], 0, [0,3,5,6,7,8,9])
+
+    with pytest.raises(ValueError, match="Error: The source node can't be a part of the targets list, since the virus is spreading from the source"):
+        non_spreading_minbudget(graphs["RegularGraph_Graph-8"], 0, [13,10,8,6,5,4,3,0,1,2])
+
+def test_save_all_vertices():
+    assert 2 == non_spreading_minbudget(graphs["RegularGraph_Graph-1"], 0, [1,2,3,4,5,6])[0] #answer is 2
+    assert 2 == non_spreading_minbudget(graphs["RegularGraph_Graph-2"], 0, [1,2,3,4,5,6,7])[0] #answer is 2
+    assert 3 != non_spreading_minbudget(graphs["RegularGraph_Graph-3"], 0, [1,2,3,4,5])[0] #answer is 2
+    assert 3 > non_spreading_minbudget(graphs["RegularGraph_Graph-4"], 0, [1,2,3,4,5,6,7])[0] #answer is 2
+    assert 1 == non_spreading_minbudget(graphs["RegularGraph_Graph-6"], 1, [0,2,3,4,5,6,7,8,9])[0] #answer is 1
+    assert 3 == non_spreading_minbudget(graphs["RegularGraph_Graph-7"], 1, [0,2,3,4,5,6])[0] #answer is 3
+    assert 2 != non_spreading_minbudget(graphs["RegularGraph_Graph-8"], 0, [1,2,3,4,5,6,7,8,9,10,11,12,13,14])[0] #answer is 3
+
+def test_save_subgroup_vertices():
+    assert 1 != non_spreading_minbudget(graphs["RegularGraph_Graph-1"], 0, [1,5,6])[0] #answer is 2
+    assert 1 == non_spreading_minbudget(graphs["RegularGraph_Graph-2"], 0, [1,3,4,5,6])[0] #answer is 1
+    assert 3 > non_spreading_minbudget(graphs["RegularGraph_Graph-3"], 0, [1,2])[0] #answer is 2
+    assert 1 < non_spreading_minbudget(graphs["RegularGraph_Graph-4"], 0, [2,3,5,7])[0] #answer is 2
+    assert 4 > non_spreading_minbudget(graphs["RegularGraph_Graph-6"], 1, [0,3,5,6,8,9])[0] #answer is 1
+    assert 2 == non_spreading_minbudget(graphs["RegularGraph_Graph-7"], 1, [0,2,5,6])[0] #answer is 2
+    assert 3 == non_spreading_minbudget(graphs["RegularGraph_Graph-8"], 0, [1,3,4,5,6,9,10,12,14])[0] #answer is 3
+
+
+if __name__ == "__main__":
+    pytest.main(["-v", __file__])
\ No newline at end of file
diff --git a/networkz/algorithms/approximation/tests/test_firefighter_problem/test_parsing.py b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_parsing.py
new file mode 100644
index 0000000..03066b8
--- /dev/null
+++ b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_parsing.py
@@ -0,0 +1,139 @@
+"""
+
+The Paper - 
+Approximability of the Firefighter Problem Computing Cuts over Time
+
+Paper Link -
+https://www.math.uwaterloo.ca/~cswamy/papers/firefighter-journ.pdf
+
+Authors - 
+Elliot Anshelevich
+Deeparnab Chakrabarty
+Ameya Hate 
+Chaitanya Swamy
+
+Developers - 
+Yuval Bubnovsky
+Almog David
+Shaked Levi
+
+"""
+
+import pytest
+import networkx as nx
+
+from networkz.algorithms.approximation.firefighter_problem.Utils import parse_json_to_networkx, Status
+
+@pytest.fixture
+def sample_json_data():
+    return {
+        "Dirlay": {
+            "Graph-1": {
+                "vertices": [0, 1, 2, 3, 4, 5],
+                "edges": [[0, 1], [0, 2]]
+            },
+        },
+        "RegularGraph": {
+            "Graph-1": {
+                "vertices": [0, 1, 2],
+                "edges": [[0, 1], [1, 2]]
+            },
+        }
+    }
+
+@pytest.fixture
+def missing_vertices_json():
+    return {
+        "InvalidGraph": {
+            "Graph-1": {
+                "edges": [[0, 1], [1, 2]]
+            }
+        }
+    }
+
+@pytest.fixture
+def missing_edges_json():
+    return {
+        "InvalidGraph": {
+            "Graph-2": {
+                "vertices": [0, 1, 2]
+            }
+        }
+    }
+
+@pytest.fixture
+def empty_json():
+    return {
+        "InvalidGraph": {
+            "Graph-3": {
+                "vertices": [],
+                "edges": []
+            }
+        }
+    }
+
+
+def test_parsing_dirlay_graph(sample_json_data):
+    graphs = parse_json_to_networkx(sample_json_data)
+
+    dirlay_graph = graphs["Dirlay_Graph-1"]
+    assert isinstance(dirlay_graph, nx.DiGraph)
+
+def test_parsing_dirlay_graph_nodes(sample_json_data):
+    graphs = parse_json_to_networkx(sample_json_data)
+
+    dirlay_graph = graphs["Dirlay_Graph-1"]
+    assert set(dirlay_graph.nodes()) == {0, 1, 2, 3, 4, 5}
+
+def test_parsing_dirlay_graph_edges(sample_json_data):
+    graphs = parse_json_to_networkx(sample_json_data)
+
+    dirlay_graph = graphs["Dirlay_Graph-1"]
+    assert set(dirlay_graph.edges()) == {(0, 1), (0, 2)}
+
+def test_parsing_regular_graph(sample_json_data):
+    graphs = parse_json_to_networkx(sample_json_data)
+
+    regular_graph = graphs["RegularGraph_Graph-1"]
+    assert isinstance(regular_graph, nx.Graph)
+
+def test_parsing_regular_graph_nodes(sample_json_data):
+    graphs = parse_json_to_networkx(sample_json_data)
+
+    regular_graph = graphs["RegularGraph_Graph-1"]
+    assert set(regular_graph.nodes()) == {0, 1, 2}
+
+def test_parsing_regular_graph_edges(sample_json_data):
+    graphs = parse_json_to_networkx(sample_json_data)
+
+    regular_graph = graphs["RegularGraph_Graph-1"]
+    assert set(regular_graph.edges()) == {(0, 1), (1, 2)}
+    
+def test_parse_exceptions_missing_vertices(missing_vertices_json):
+    with pytest.raises(KeyError):
+        parse_json_to_networkx(missing_vertices_json)
+
+def test_parse_exceptions_missing_edges(missing_edges_json):
+    with pytest.raises(KeyError):
+        parse_json_to_networkx(missing_edges_json)
+
+def test_parse_exceptions_empty_json(empty_json):
+    with pytest.raises(KeyError):
+        parse_json_to_networkx(empty_json)
+        
+def test_parsing_dirlay_graph_status(sample_json_data):
+    graphs = parse_json_to_networkx(sample_json_data)
+
+    dirlay_graph = graphs["Dirlay_Graph-1"]
+    for node in dirlay_graph.nodes(data=True):
+        assert node[1]["status"] == Status.VULNERABLE.value
+
+def test_parsing_regular_graph_status(sample_json_data):
+    graphs = parse_json_to_networkx(sample_json_data)
+
+    regular_graph = graphs["RegularGraph_Graph-1"]
+    for node in regular_graph.nodes(data=True):
+        assert node[1]["status"] == Status.VULNERABLE.value
+
+if __name__ == "__main__":
+    pytest.main(["-v", __file__])
\ No newline at end of file
diff --git a/networkz/algorithms/approximation/tests/test_firefighter_problem/test_spreading_maxsave.py b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_spreading_maxsave.py
new file mode 100644
index 0000000..15b7873
--- /dev/null
+++ b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_spreading_maxsave.py
@@ -0,0 +1,299 @@
+"""
+
+The Paper - 
+Approximability of the Firefighter Problem Computing Cuts over Time
+
+Paper Link -
+https://www.math.uwaterloo.ca/~cswamy/papers/firefighter-journ.pdf
+
+Authors - 
+Elliot Anshelevich
+Deeparnab Chakrabarty
+Ameya Hate 
+Chaitanya Swamy
+
+Developers - 
+Yuval Bubnovsky
+Almog David
+Shaked Levi
+
+"""
+
+import pytest
+import networkx as nx
+import json
+import random
+import os
+
+from networkz.algorithms.approximation.firefighter_problem.Firefighter_Problem import spreading_maxsave
+from networkz.algorithms.approximation.firefighter_problem.Utils import parse_json_to_networkx, calculate_gamma, calculate_epsilon, find_best_direct_vaccination
+
+path_to_graphs = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'graphs.json')
+if os.path.exists(path_to_graphs):
+    with open(path_to_graphs, "r") as file:
+        json_data = json.load(file)
+else:
+    raise FileNotFoundError(f"{path_to_graphs} does not exist.")
+graphs = parse_json_to_networkx(json_data)
+
+@pytest.mark.parametrize("graph_key, budget, source, targets", [
+    ("RegularGraph_Graph-1", 1, -2, [1, 2, 3, 4, 5, 6]),
+    ("RegularGraph_Graph-4", 1, 8, [1, 2, 4, 6, 7]),
+    ("RegularGraph_Graph-6", 1, 10, [0, 2, 3, 5, 6, 7, 8, 9]),
+    ("RegularGraph_Graph-8", 1, 17, [1, 7, 12, 14, 8, 3, 11, 2]),
+    ("RegularGraph_Graph-3", 1, 6, [1, 3, 5]),
+])
+def test_source_not_in_graph(graph_key, budget, source, targets):
+    with pytest.raises(ValueError):
+        spreading_maxsave(graphs[graph_key], budget, source, targets)
+
+@pytest.mark.parametrize("graph_key, budget, source, targets", [
+    ("RegularGraph_Graph-2", 1, 0, [1, 2, 3, 9, 5, 16]),
+    ("RegularGraph_Graph-3", 1, 4, [1, 2, 3, 6, 7]),
+    ("RegularGraph_Graph-6", 1, 3, [0, 2, 5, 6, 7, 8, 10]),
+    ("RegularGraph_Graph-8", 1, 11, [1, 3, 12, 19, 8, 10, 4, 2]),
+    ("RegularGraph_Graph-7", 1, 2, [1, 3, -1, 5]),
+])
+def test_target_not_in_graph(graph_key, budget, source, targets):
+    with pytest.raises(ValueError):
+        spreading_maxsave(graphs[graph_key], budget, source, targets)
+
+@pytest.mark.parametrize("graph_key, budget, source, targets", [
+    ("RegularGraph_Graph-1", 1, 0, [1, 2, 3, 0, 4, 5, 6]),
+    ("RegularGraph_Graph-3", 1, 1, [5, 1, 4]),
+    ("RegularGraph_Graph-4", 1, 4, [1, 2, 3, 4, 5, 6, 7]),
+    ("RegularGraph_Graph-6", 1, 0, [0, 3, 5, 6, 7, 8, 9]),
+    ("RegularGraph_Graph-8", 1, 0, [13, 10, 8, 6, 5, 4, 3, 0, 1, 2]),
+])
+def test_source_is_target(graph_key, budget, source, targets):
+    with pytest.raises(ValueError):
+        spreading_maxsave(graphs[graph_key], budget, source, targets)
+
+@pytest.mark.parametrize("graph_key, source, targets, expected_gamma, expected_direct_vaccination", [
+    ("Dirlay_Graph-5", 0, [1, 2, 3, 4, 5 ,6 ,7 ,8], {
+        1: [(2, 1), (4, 1), (1, 1), (1, 2)],
+        2: [(2, 1)],
+        3: [(2, 1), (5, 1), (3, 1), (3, 2)],
+        4: [(4, 1)],
+        5: [(5, 1)],
+        6: [(4, 1), (5, 1), (6, 1), (6, 2)],
+        7: [(5, 1), (6, 1), (7, 1), (7, 2)],
+        8: [(4, 1), (5, 1), (6, 1), (6, 2), (7, 1), (7, 2), (8, 1), (8, 2), (8, 3)],
+    }, {
+        (1, 1): [1],
+        (1, 2): [1],
+        (2, 1): [1, 2, 3],
+        (3, 1): [3],
+        (3, 2): [3],
+        (4, 1): [1, 4, 6, 8],
+        (5, 1): [3, 5, 6, 7, 8],
+        (6, 1): [6, 7, 8],
+        (6, 2): [6, 8],
+        (7, 1): [7, 8],
+        (7, 2): [7, 8],
+        (8, 1): [8],
+        (8, 2): [8],
+        (8, 3): [8]
+    }),
+    ("RegularGraph_Graph-1", 0, [1, 3, 4, 5], {
+        1: [(1, 1)],
+        2: [(2, 1)],
+        3: [(1, 1), (2, 1), (3, 1), (3, 2)],
+        4: [(1, 1), (4, 1), (4, 2)],
+        5: [(1, 1), (2, 1), (3, 1), (3, 2), (5, 1), (5, 2), (5, 3)],
+        6: [(2, 1), (6, 1), (6, 2)],
+    }, {
+        (1, 1): [1, 3, 4, 5],
+        (2, 1): [3, 5],
+        (3, 1): [3, 5],
+        (3, 2): [3, 5],
+        (4, 1): [4],
+        (4, 2): [4],
+        (5, 1): [5],
+        (5, 2): [5],
+        (5, 3): [5],
+        (6, 1): [],
+        (6, 2): [],
+    })
+])
+def test_calculate_gamma(graph_key, source, targets, expected_gamma, expected_direct_vaccination):
+    print(calculate_gamma(graphs[graph_key], source, targets))
+    calculated_gamma, calculated_direct_vaccination = calculate_gamma(graphs[graph_key], source, targets)
+    
+    for key in expected_gamma:
+        assert key in calculated_gamma, f"Expected key {key} to be in {calculated_gamma}"
+    assert calculated_direct_vaccination == expected_direct_vaccination
+
+@pytest.mark.parametrize("direct_vaccinations, expected_epsilon", [
+    ({
+        (1, 1): [1, 3, 4, 5],
+        (2, 1): [2, 3, 5, 6],
+        (3, 1): [3, 5],
+        (3, 2): [3, 5],
+        (4, 1): [4],
+        (4, 2): [4],
+        (5, 1): [5],
+        (5, 2): [5],
+        (5, 3): [5],
+        (6, 1): [6],
+        (6, 2): [6],
+    }, [
+        [(1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)],
+        [(3, 2), (4, 2), (5, 2), (6, 2)],
+        [(5, 3)]
+    ]),
+    ({
+        (1, 1): [1],
+        (1, 2): [1],
+        (2, 1): [1, 2, 3],
+        (3, 1): [3],
+        (3, 2): [3],
+        (4, 1): [1, 4, 6, 8],
+        (5, 1): [3, 5, 6, 7, 8],
+        (6, 1): [4, 6, 8],
+        (6, 2): [6, 8],
+        (7, 1): [7, 8],
+        (7, 2): [7, 8],
+        (8, 1): [8],
+        (8, 2): [8],
+        (8, 3): [8],
+    }, [
+        [(1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (7, 1), (8, 1)],
+        [(1, 2), (3, 2), (6, 2), (7, 2), (8, 2)],
+        [(8, 3)]
+    ]),
+])
+def test_calculate_epsilon(direct_vaccinations, expected_epsilon):
+    calculated_epsilon = calculate_epsilon(direct_vaccinations)
+    
+    assert calculated_epsilon == expected_epsilon
+
+@pytest.mark.parametrize("graph_key, direct_vaccinations, current_epsilon, targets, expected_best_direct_vaccination", [
+    ("RegularGraph_Graph-1",
+     {
+     (1, 1): [1, 2, 3, 4, 5, 7],
+        (2, 1): [2, 3, 4, 7],
+        (2, 2): [2, 3, 7],
+        (3, 1): [3, 4, 7],
+        (3, 2): [3, 4, 7],
+        (3, 3): [3, 7],
+        (4, 1): [4, 7],
+        (4, 2): [4, 7],
+        (4, 3): [4, 7],
+        (5, 1): [2, 3, 4, 5, 7],
+        (5, 2): [3, 4, 5, 7],
+        (6, 1): [3, 4, 5, 6, 7],
+    }, 
+    [(1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)],
+    [1, 3, 4, 5, 6], 
+    (1, 1)),
+    ("Dirlay_Graph-5", 
+     {
+        (1, 1): [1],
+        (1, 2): [1],
+        (2, 1): [1, 2, 3],
+        (3, 1): [3],
+        (3, 2): [3],
+        (4, 1): [1, 4, 6, 8],
+        (5, 1): [3, 5, 6, 7, 8],
+        (6, 1): [4, 6, 8],
+        (6, 2): [6, 8],
+        (7, 1): [7, 8],
+        (7, 2): [7, 8],
+        (8, 1): [8],
+        (8, 2): [8],
+        (8, 3): [8],
+    }, 
+    [(1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (7, 1), (8, 1)],
+    [1, 2, 3, 4, 5, 6, 7, 8],
+    (5, 1))
+])
+  
+def test_find_best_direct_vaccination(graph_key, direct_vaccinations, current_epsilon, targets, expected_best_direct_vaccination):
+    calculated_best_direct_vaccination = find_best_direct_vaccination(graphs[graph_key],direct_vaccinations,current_epsilon,targets)[0]
+    
+    assert calculated_best_direct_vaccination == expected_best_direct_vaccination
+
+@pytest.mark.parametrize("graph_key, budget, source, targets, expected_length", [
+    ("RegularGraph_Graph-1", 1, 0, [1, 2, 3, 4, 5, 6], 2),
+    ("Dirlay_Graph-5", 2, 0, [1, 2, 3, 4, 5, 6, 7, 8], 3),
+])
+def test_strategy_length(graph_key, budget, source, targets, expected_length):
+    graph = graphs[graph_key]
+    calculated_strategy = spreading_maxsave(graph, budget, source, targets)[0]
+    
+    assert len(calculated_strategy) == expected_length
+
+
+@pytest.mark.parametrize("graph_key, budget, source, targets, expected_strategy", [
+    ("RegularGraph_Graph-1", 1, 0, [1, 2, 3, 4, 5, 6], [(1, 1), (6, 2)]),
+    ("Dirlay_Graph-5", 2, 0, [1, 2, 3, 4, 5, 6, 7, 8], [(5, 1), (2, 1), (8, 2)]),
+])
+def test_save_all_vertices(graph_key, budget, source, targets, expected_strategy):
+    graph = graphs[graph_key]
+    calculated_strategy = spreading_maxsave(graph, budget, source, targets)[0]
+    
+    assert calculated_strategy == expected_strategy
+
+@pytest.mark.parametrize("graph_key, budget, source, targets, expected_strategy", [
+    ("RegularGraph_Graph-6", 2, 1, [3, 9, 0, 5, 6], [(2, 1), (0, 1)]),
+    ("RegularGraph_Graph-4", 1, 0, [2, 6, 4], [(1, 1), (3, 2)]),
+])
+def test_save_subgroup_vertices(graph_key, budget, source, targets, expected_strategy):
+    graph = graphs[graph_key]
+    calculated_strategy = spreading_maxsave(graph, budget, source, targets)[0]
+    
+    assert calculated_strategy == expected_strategy
+
+@pytest.mark.parametrize("graph_key, budget, source, targets, expected_nodes_saved_list", [
+    ("RegularGraph_Graph-1", 1, 0, [1, 2, 3, 4, 5, 6], {1, 3, 4, 5, 6}),
+    ("Dirlay_Graph-5", 2, 0, [1, 2, 3, 4, 5, 6, 7, 8], {1, 2, 3, 5, 6, 7, 8}),
+])
+def test_save_all_vertices_nodes_list(graph_key, budget, source, targets, expected_nodes_saved_list):
+    graph = graphs[graph_key]
+    calculated_nodes_saved_list = spreading_maxsave(graph, budget, source, targets)[1]
+    print(calculated_nodes_saved_list)
+    
+    assert calculated_nodes_saved_list == expected_nodes_saved_list
+
+@pytest.mark.parametrize("graph_key, budget, source, targets, expected_nodes_saved_list", [
+    ("RegularGraph_Graph-6", 2, 1, [3, 9, 0, 5, 6], {0, 3, 5, 6, 9}),
+    ("RegularGraph_Graph-4", 1, 0, [2, 6, 4], {2, 4}),
+])
+def test_save_subgroup_vertices_nodes_list(graph_key, budget, source, targets, expected_nodes_saved_list):
+    graph = graphs[graph_key]
+    calculated_nodes_saved_list = spreading_maxsave(graph, budget, source, targets)[1]
+    
+    assert calculated_nodes_saved_list == expected_nodes_saved_list
+
+def test_random_graph():
+    for i in range(10):
+        num_nodes = random.randint(2,100)
+        nodes = list(range(num_nodes+1))
+        num_edges = 1000
+        save_amount = random.randint(1,num_nodes)
+        targets = []
+        G = nx.DiGraph()
+        
+        G.add_nodes_from(nodes, status="target")
+        for _ in range(num_edges):
+            source = random.randint(0, num_nodes - 1)
+            target = random.randint(0, num_nodes - 1)
+            if source != target:  # Ensure no self-loops
+                G.add_edge(source, target)
+        for node in range(save_amount):
+            probability = random.random()
+            if probability < 0.75 and node!=0:
+                targets.append(node)
+        
+        ans = spreading_maxsave(G,1,0,targets)[0]
+        print(len(ans))
+        print(len(G.nodes))
+       
+        assert len(ans) <= len(G.nodes)
+    
+    print("All tests have passed!")
+
+
+if __name__ == "__main__":
+    pytest.main(["-v", __file__])
\ No newline at end of file
diff --git a/networkz/algorithms/approximation/tests/test_firefighter_problem/test_spreading_minbudget.py b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_spreading_minbudget.py
new file mode 100644
index 0000000..29c9865
--- /dev/null
+++ b/networkz/algorithms/approximation/tests/test_firefighter_problem/test_spreading_minbudget.py
@@ -0,0 +1,291 @@
+"""
+
+The Paper - 
+Approximability of the Firefighter Problem Computing Cuts over Time
+
+Paper Link -
+https://www.math.uwaterloo.ca/~cswamy/papers/firefighter-journ.pdf
+
+Authors - 
+Elliot Anshelevich
+Deeparnab Chakrabarty
+Ameya Hate 
+Chaitanya Swamy
+
+Developers - 
+Yuval Bubnovsky
+Almog David
+Shaked Levi
+
+"""
+
+import pytest
+import json
+import random
+import os
+
+from networkz.algorithms.approximation.firefighter_problem.Firefighter_Problem import spreading_minbudget
+from networkz.algorithms.approximation.firefighter_problem.Utils import parse_json_to_networkx, calculate_gamma, calculate_epsilon, find_best_direct_vaccination
+from networkz.algorithms.approximation.firefighter_problem.Random_Graph_Generator import generate_random_DiGraph
+
+
+@pytest.fixture
+def sample_json_data():
+    return {
+        "Dirlay": {
+            "Graph-1": {
+                "vertices": [0, 1, 2, 3, 4, 5],
+                "edges": [[0, 1], [0, 2]]
+            },
+        },
+        "RegularGraph": {
+            "Graph-1": {
+                "vertices": [0, 1, 2],
+                "edges": [[0, 1], [1, 2]]
+            },
+        }
+    }
+
+def get_graphs():
+    path_to_graphs = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'graphs.json')
+    if os.path.exists(path_to_graphs):
+        with open(path_to_graphs, "r") as file:
+            json_data = json.load(file)
+    else:
+        raise FileNotFoundError(f"{path_to_graphs} does not exist.")
+    
+    graphs = parse_json_to_networkx(json_data)
+    return graphs
+
+graphs =  get_graphs()
+    
+def test_source_not_in_graph():
+    with pytest.raises(ValueError, match="Error: The source node isn't on the graph"):
+        spreading_minbudget(graphs["RegularGraph_Graph-1"], -3, [1,0,4,5,2,6])
+
+    with pytest.raises(ValueError, match="Error: The source node isn't on the graph"):
+        spreading_minbudget(graphs["RegularGraph_Graph-4"], 10, [1,3,5,6,7])
+
+    with pytest.raises(ValueError, match="Error: The source node isn't on the graph"):
+        spreading_minbudget(graphs["RegularGraph_Graph-6"], 12, [9,2,3,4,6,7])
+
+    with pytest.raises(ValueError, match="Error: The source node isn't on the graph"):
+        spreading_minbudget(graphs["RegularGraph_Graph-8"], -1, [7,10,4,9,3,11,2])
+
+    with pytest.raises(ValueError, match="Error: The source node isn't on the graph"):
+        spreading_minbudget(graphs["RegularGraph_Graph-3"], 8, [1,4,2])
+        
+
+def test_target_not_in_graph():
+    with pytest.raises(ValueError, match="Error: Not all nodes in the targets list are on the graph."):
+        spreading_minbudget(graphs["RegularGraph_Graph-2"], 2, [0,4,5,11,6])
+
+    with pytest.raises(ValueError, match="Error: Not all nodes in the targets list are on the graph."):
+        spreading_minbudget(graphs["RegularGraph_Graph-3"], 3, [0,4,5,-1,1,2])
+
+    with pytest.raises(ValueError, match="Error: Not all nodes in the targets list are on the graph."):
+        spreading_minbudget(graphs["RegularGraph_Graph-6"], 7, [9,2,4,5,8,11])
+
+    with pytest.raises(ValueError, match="Error: Not all nodes in the targets list are on the graph."):
+        spreading_minbudget(graphs["RegularGraph_Graph-8"], 10, [0,2,4,5,8,11,12,3,15])
+
+    with pytest.raises(ValueError, match="Error: Not all nodes in the targets list are on the graph."):
+        spreading_minbudget(graphs["RegularGraph_Graph-7"], 1, [3,5,4,0,13])
+        
+
+def test_source_is_target():
+    with pytest.raises(ValueError, match="Error: The source node can't be a part of the targets list, since the virus is spreading from the source"):
+        spreading_minbudget(graphs["RegularGraph_Graph-1"], 0, [1,2,3,0,4,5,6])
+    
+    with pytest.raises(ValueError, match="Error: The source node can't be a part of the targets list, since the virus is spreading from the source"):
+        spreading_minbudget(graphs["RegularGraph_Graph-3"], 1, [5,1,4])
+    
+    with pytest.raises(ValueError, match="Error: The source node can't be a part of the targets list, since the virus is spreading from the source"):
+        spreading_minbudget(graphs["RegularGraph_Graph-4"], 4, [1,2,3,4,5,6,7])
+    
+    with pytest.raises(ValueError, match="Error: The source node can't be a part of the targets list, since the virus is spreading from the source"):
+        spreading_minbudget(graphs["RegularGraph_Graph-6"], 0, [0,3,5,6,7,8,9])
+
+    with pytest.raises(ValueError, match="Error: The source node can't be a part of the targets list, since the virus is spreading from the source"):
+        spreading_minbudget(graphs["RegularGraph_Graph-8"], 0, [13,10,8,6,5,4,3,0,1,2])
+
+@pytest.mark.parametrize("graph_key, source, targets, expected_gamma, expected_direct_vaccination", [
+    ("RegularGraph_Graph-4", 0, [1, 2, 3, 4, 5 ,6 ,7], {
+        1: [(1, 1)],
+        2: [(1, 1), (2, 1), (2, 2), (5, 1)],
+        3: [(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3), (5, 1), (5, 2), (6, 1)],
+        4: [(1, 1), (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (6, 1)],
+        5: [(1, 1), (5, 1), (5, 2), (6, 1)],
+        6: [(6, 1)],
+        7: [],
+    }, {
+        (1, 1): [1, 2, 3, 4, 5, 7],
+        (2, 1): [2, 3, 4, 7],
+        (2, 2): [2, 3, 7],
+        (3, 1): [3, 4, 7],
+        (3, 2): [3, 4, 7],
+        (3, 3): [3, 7],
+        (4, 1): [4, 7],
+        (4, 2): [4, 7],
+        (4, 3): [4, 7],
+        (5, 1): [2, 3, 4, 5, 7],
+        (5, 2): [3, 4, 5, 7],
+        (6, 1): [3, 4, 5, 6, 7]
+    }),
+    ("RegularGraph_Graph-1", 0, [1, 3, 4, 5], {
+        1: [(1, 1)],
+        2: [(2, 1)],
+        3: [(1, 1), (2, 1), (3, 1), (3, 2)],
+        4: [(1, 1), (4, 1), (4, 2)],
+        5: [(1, 1), (2, 1), (3, 1), (3, 2), (5, 1), (5, 2), (5, 3)],
+        6: [(2, 1), (6, 1), (6, 2)],
+    }, {
+        (1, 1): [1, 3, 4, 5],
+        (2, 1): [3, 5],
+        (3, 1): [3, 5],
+        (3, 2): [3, 5],
+        (4, 1): [4],
+        (4, 2): [4],
+        (5, 1): [5],
+        (5, 2): [5],
+        (5, 3): [5],
+        (6, 1): [],
+        (6, 2): [],
+    })
+])
+def test_calculate_gamma(graph_key, source, targets, expected_gamma, expected_direct_vaccination):
+    calculated_gamma, calculated_direct_vaccination = calculate_gamma(graphs[graph_key], source, targets)
+    
+    assert calculated_gamma == expected_gamma
+    assert calculated_direct_vaccination == expected_direct_vaccination
+
+
+@pytest.mark.parametrize("direct_vaccinations, expected_epsilon", [
+    ({
+        (1, 1): [1, 2, 3, 4, 5, 7],
+        (2, 1): [2, 3, 4, 7],
+        (2, 2): [2, 3, 7],
+        (3, 1): [3, 4, 7],
+        (3, 2): [3, 4, 7],
+        (3, 3): [3, 7],
+        (4, 1): [4, 7],
+        (4, 2): [4, 7],
+        (4, 3): [4, 7],
+        (5, 1): [2, 3, 4, 5, 7],
+        (5, 2): [3, 4, 5, 7],
+        (6, 1): [3, 4, 5, 6, 7],
+    }, [
+        [(1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)],
+        [(2, 2), (3, 2), (4, 2), (5, 2)],
+        [(3, 3), (4, 3)]
+    ]),
+    ({
+        (1, 1): [1],
+        (1, 2): [1],
+        (2, 1): [1, 2, 3],
+        (3, 1): [3],
+        (3, 2): [3],
+        (4, 1): [1, 4, 6, 8],
+        (5, 1): [3, 5, 6, 7, 8],
+        (6, 1): [4, 6, 8],
+        (6, 2): [6, 8],
+        (7, 1): [7, 8],
+        (7, 2): [7, 8],
+        (8, 1): [8],
+        (8, 2): [8],
+        (8, 3): [8],
+    }, [
+        [(1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (7, 1), (8, 1)],
+        [(1, 2), (3, 2), (6, 2), (7, 2), (8, 2)],
+        [(8, 3)]
+    ]),
+])
+def test_calculate_epsilon(direct_vaccinations, expected_epsilon):
+    calculated_epsilon = calculate_epsilon(direct_vaccinations)
+    
+    assert calculated_epsilon == expected_epsilon
+
+@pytest.mark.parametrize("graph_key, direct_vaccinations, current_epsilon, targets, expected_best_direct_vaccination", [
+    ("RegularGraph_Graph-1",
+     {
+        (1, 1): [1, 2, 3, 4, 5, 7],
+        (2, 1): [2, 3, 4, 7],
+        (2, 2): [2, 3, 7],
+        (3, 1): [3, 4, 7],
+        (3, 2): [3, 4, 7],
+        (3, 3): [3, 7],
+        (4, 1): [4, 7],
+        (4, 2): [4, 7],
+        (4, 3): [4, 7],
+        (5, 1): [2, 3, 4, 5, 7],
+        (5, 2): [3, 4, 5, 7],
+        (6, 1): [3, 4, 5, 6, 7],
+    }, 
+    [(1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)],
+    [1, 3, 4, 5, 6], 
+    (1, 1)),
+    ("Dirlay_Graph-5", 
+     {
+        (1, 1): [1],
+        (1, 2): [1],
+        (2, 1): [1, 2, 3],
+        (3, 1): [3],
+        (3, 2): [3],
+        (4, 1): [1, 4, 6, 8],
+        (5, 1): [3, 5, 6, 7, 8],
+        (6, 1): [4, 6, 8],
+        (6, 2): [6, 8],
+        (7, 1): [7, 8],
+        (7, 2): [7, 8],
+        (8, 1): [8],
+        (8, 2): [8],
+        (8, 3): [8],
+    }, 
+    [(1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (7, 1), (8, 1)],
+    [1, 2, 3, 4, 5, 6, 7, 8],
+    (5, 1))
+])
+    
+def test_find_best_direct_vaccination(graph_key, direct_vaccinations, current_epsilon, targets, expected_best_direct_vaccination):
+    calculated_best_direct_vaccination = find_best_direct_vaccination(graphs[graph_key],direct_vaccinations,current_epsilon,targets)[0]
+    
+    assert calculated_best_direct_vaccination == expected_best_direct_vaccination
+
+def test_save_all_vertices():
+    assert 2 == spreading_minbudget(graphs["RegularGraph_Graph-1"], 0, [1,2,3,4,5,6])[0] # answer is 2
+    assert 2 == spreading_minbudget(graphs["RegularGraph_Graph-2"], 0, [1,2,3,4,5,6,7])[0] # answer is 2
+    assert 3 != spreading_minbudget(graphs["RegularGraph_Graph-3"], 0, [1,2,3,4,5])[0] # answer is 2
+    assert spreading_minbudget(graphs["RegularGraph_Graph-2"], 0, [1,2,3,4,5,6,7])[0] >= spreading_minbudget(graphs["RegularGraph_Graph-4"], 0, [1,2,3,4,5,6,7])[0] # answer is 2 
+    assert spreading_minbudget(graphs["RegularGraph_Graph-1"], 0, [1,2,3,4,5,6])[0] > spreading_minbudget(graphs["RegularGraph_Graph-6"], 1, [0,2,3,4,5,6,7,8,9])[0] # answer is 1
+    assert 3 == spreading_minbudget(graphs["RegularGraph_Graph-7"], 1, [0,2,3,4,5,6])[0] # answer is 3 
+    assert 2 != spreading_minbudget(graphs["RegularGraph_Graph-8"], 0, [1,2,3,4,5,6,7,8,9,10,11,12,13,14])[0] # answer is 4
+    
+
+def test_save_subgroup_vertices():
+    assert spreading_minbudget(graphs["RegularGraph_Graph-1"], 0, [1,2,3,4,5,6])[0] != spreading_minbudget(graphs["RegularGraph_Graph-1"], 0, [1,5,6])[0] # answer is 1 
+    assert 1 == spreading_minbudget(graphs["RegularGraph_Graph-2"], 0, [1,3,4,5,6])[0] #answer is 1 
+    assert spreading_minbudget(graphs["RegularGraph_Graph-3"], 0, [1,2,3,4,5])[0] > spreading_minbudget(graphs["RegularGraph_Graph-3"], 0, [1,3,5])[0] #answer is 1
+    assert 2 > spreading_minbudget(graphs["RegularGraph_Graph-4"], 0, [2,3,5,7])[0] # anser is 1 
+    assert 4 > spreading_minbudget(graphs["RegularGraph_Graph-6"], 1, [0,3,5,6,8,9])[0] #answer is 1 
+    assert 2 == spreading_minbudget(graphs["RegularGraph_Graph-7"], 1, [4,2,5,6])[0] #answer is 2 
+    assert spreading_minbudget(graphs["RegularGraph_Graph-8"], 0, [1,2,3,4,5,6,7,8,9,10,11,12,13,14])[0] != spreading_minbudget(graphs["RegularGraph_Graph-8"], 0, [1,3,4,5,6,9,10,12,14])[0] #answer is 3
+
+
+def test_random_graph():
+    for i in range(10):
+        G =  generate_random_DiGraph(num_nodes=100, edge_probability=0.5)
+
+        num_targets = random.randint(1, int(len(G.nodes) / 2) + 1)
+        nodes_to_sample = list(G.nodes)
+        nodes_to_sample.remove(0)
+        targets = random.sample(nodes_to_sample, num_targets)
+        
+        target_length = len(targets)
+        ans = spreading_minbudget(G,0,targets)[0]
+
+        assert ans <= target_length
+    
+    print("All tests have passed!")
+
+if __name__ == "__main__":
+    pytest.main(["-v", __file__])
\ No newline at end of file
diff --git a/networkz/algorithms/max_flow_with_node_capacity.py b/networkz/algorithms/max_flow_with_node_capacity.py
new file mode 100644
index 0000000..89997a1
--- /dev/null
+++ b/networkz/algorithms/max_flow_with_node_capacity.py
@@ -0,0 +1,113 @@
+"""
+
+The Paper - 
+Approximability of the Firefighter Problem Computing Cuts over Time
+
+Paper Link -
+https://www.math.uwaterloo.ca/~cswamy/papers/firefighter-journ.pdf
+
+Authors - 
+Elliot Anshelevich
+Deeparnab Chakrabarty
+Ameya Hate 
+Chaitanya Swamy
+
+Developers - 
+Yuval Bubnovsky
+Almog David
+Shaked Levi
+
+"""
+
+import networkx as nx
+import networkx.algorithms.connectivity as algo 
+from networkz.algorithms.approximation.firefighter_problem.Utils import *
+import logging
+
+
+logger = logging.getLogger(__name__)
+
+def min_cut_with_node_capacity(graph: nx.DiGraph, source: int = None, target: int = None) -> set:
+    """
+    Computes a minimum cut in the given graph, where each node has a capacity
+
+    Parameters:
+    ----------
+    graph : nx.DiGraph
+        The original directed graph. Each node should have a 'capacity' attribute.
+    source (Optional) : int
+        The source node in the graph. This node will have an infinite capacity 
+        between its "in" and "out" nodes.
+    target (Optional) : int
+        The target node in the graph. This node will have an infinite capacity 
+        between its "in" and "out" nodes
+
+    Returns:
+    -------
+    set
+       The minimum cut nodes 
+
+    Notes:
+    -----
+    This function transforms a given directed graph into a new graph where each node
+    is split into two nodes (an "in" node and an "out" node) connected by an edge 
+    with a capacity (weight). The transformation is used for flow problems where 
+    nodes have capacities instead of edges - allowing to run algorithms which
+    were originally designed to be used for edge-flow problems.
+    - If a node does not have a 'capacity' attribute, a default capacity of 1 
+      is used.
+    - There is infinite capacity between two different edge_out & edge_in
+
+    Examples:
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_node(1, capacity=0.6)
+    >>> G.add_node(2, capacity=0.6)
+    >>> G.add_node(3, capacity=0.3)
+    >>> G.add_node(4, capacity=0.3)
+    >>> G.add_edge(0, 1)
+    >>> G.add_edge(0, 2)
+    >>> G.add_edge(2, 3)
+    >>> G.add_edge(1, 4)
+    >>> s_t_G = create_st_graph(G, [2,4], 't')
+    >>> min_cut_nodes = min_cut_with_node_capacity(s_t_G, 0, 4)
+    >>> sorted(min_cut_nodes)
+    ['2_out', '4_out']
+    """
+    logger.info("Starting graph flow reduction")
+    H = nx.DiGraph()
+    
+    logger.debug("Adding nodes and internal edges")
+    for node in graph.nodes:
+        in_node, out_node = f'{node}_in', f'{node}_out'
+        H.add_nodes_from([in_node, out_node])
+        if node == source:
+            H.add_edge(in_node, out_node, weight=float('inf'))
+            logger.debug(f"Added infinite capacity edge for source node: {node}")
+        elif node == target:
+            H.add_edge(in_node, out_node, weight=float('inf'))
+            logger.debug(f"Added infinite capacity edge for target node: {node}")
+        else:
+            capacity = graph.nodes[node].get('capacity', 1)
+            H.add_edge(in_node, out_node, weight=capacity)
+            logger.debug(f"Added edge with capacity {capacity} for node: {node}")
+    
+    logger.debug("Adding edges between nodes")
+    for edge in graph.edges:
+        u_out, v_in = f'{edge[0]}_out', f'{edge[1]}_in'
+        H.add_edge(u_out, v_in, weight=float('inf'))
+        logger.debug(f"Added infinite capacity edge from {u_out} to {v_in}")
+    
+    logger.info("Graph flow reduction finished")
+
+    # Compute the minimum cut
+    logger.info(f"Finding the minimum cut on the graph after reduction") 
+    min_cut_nodes = algo.minimum_st_node_cut(H, f'{source}_out', 't_in')
+    
+    logger.info(f"Minimum Cut is: {min_cut_nodes}")  
+    return min_cut_nodes
+
+if __name__ == "__main__":
+    import doctest
+    result = doctest.testmod(verbose=False)
+    print(f"Doctest results: {result}")
diff --git a/pyproject.toml b/pyproject.toml
index 4c057b2..a310b1f 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -95,3 +95,7 @@ select = [
 [tool.mypy]
 ignore_missing_imports = true
 exclude = 'subgraphviews|reportviews'
+
+[tool.pytest.ini_options]
+minversion = "6.0"
+addopts = " --doctest-modules --durations=10 --ignore=experiments"