example_function_uses.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "728f43c2",
   "metadata": {},
   "source": [
    "# Example Uses of Function in `tree_augmentation`\n",
    "In this notebook, we present the most important functions from the `tree_augmentation` module. For further details, consult the docstrings of the functions.\n",
    "### Loading functions\n",
    "All modules and functions can be loaded by simply loading the `tree_augmentation.comparisons` file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "00e5129d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tree_augmentation.comparisons import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50946cf2",
   "metadata": {},
   "source": [
    "### General functions\n",
    "All functions assume that we work with NetworkX graphs. See below how we can define and draw graphs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b46d6c32",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We can either define a random tree\n",
    "T = nx.random_tree(10, seed = 1234)\n",
    "\n",
    "# or we can define a tree from an edgeset\n",
    "edgeset = [(0, 4), (0, 7), (0, 1), (1, 3), (1, 5), (1, 8), (1, 9), (2, 7), (6, 9)]\n",
    "T = nx.Graph(edgeset)\n",
    "\n",
    "# we can generate a set of links using the generate_random_links_by_type function defined in tree_augmentation.general\n",
    "# we can also define what type of links to include (c = crosslinks, i = inlinks, u = uplinks).\n",
    "L = generate_random_links_by_type(tree = T, root = 0, types_to_include = ['c', 'i', 'u'], number_links = 5, seed = 4321)\n",
    "\n",
    "# we can draw a tree using the draw_tree function defined in tree_augmentation.general\n",
    "draw_tree(tree = T, root = 0, links = L)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95baf2ba",
   "metadata": {},
   "source": [
    "In all numerical simulations, we generate the same instances in order to get comparable results. Once we specify a tree size `n`, the parameter `factor` that controls the size of the link set, and the random seed `seed`, we get a unique TAP instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c43800b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T, L = get_instance(n = 10, factor = 2, seed = 7)\n",
    "draw_tree(tree = T, root = 0, links = L)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3211a94e",
   "metadata": {},
   "source": [
    "All functions defined in `tree_augmentation` have a docstring. We can hence ask for help whenever needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "13bcacf8",
   "metadata": {},
   "outputs": [],
   "source": [
    "get_instance?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b679c0bc",
   "metadata": {},
   "source": [
    "### Natural LP\n",
    "The following function allows us to solve the natural LP relaxation. If we specify `variable_type = GRB.BINARY`, then the integer IP is solved (i.e. we obtain the exact solution), and if `variable_type = GRB.CONTINUOUS` is specified, then we compute the natural LP relaxation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "72f6d415",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'lp_status': 'opt',\n",
       " 'optimal_solution': [0.0,\n",
       "  0.0,\n",
       "  0.3333333333333333,\n",
       "  0.0,\n",
       "  0.0,\n",
       "  0.0,\n",
       "  0.0,\n",
       "  0.3333333333333333,\n",
       "  0.0,\n",
       "  0.6666666666666667,\n",
       "  0.0,\n",
       "  0.0,\n",
       "  0.0,\n",
       "  0.6666666666666667,\n",
       "  0.3333333333333333,\n",
       "  0.0,\n",
       "  0.0,\n",
       "  0.0],\n",
       " 'optimal_obj_value': 2.3333333333333335}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve_naturalLP(tree = T, links = L, link_weights = None, variable_type = GRB.CONTINUOUS)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d9261bc",
   "metadata": {},
   "source": [
    "### Solve using approximation algorithms\n",
    "Below we show how to solve the TAP using the approximation algorithms defined. Note that we have to add the following prefixes to our functions:\n",
    "- `nrd.` for the naive rounding procedure\n",
    "- `ird.` for the iterative roudning procedure\n",
    "- `upl.` for the approximation via uplinks\n",
    "- `mat.` fot the approximation using the matching heuristic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "50ffcc43",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'status': 'opt', 'optimal_solution': [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0], 'optimal_obj_value': 3, 'selected_in_order': [(4, 7), (3, 9), (0, 3)], 'selected_links_orig_form': [(4, 7), (3, 9), (2, 9)]}\n"
     ]
    }
   ],
   "source": [
    "# solve via naive rounding\n",
    "sol_nrd = nrd.approximation_via_naiveRounding(tree = T, links = L, link_weights = None)\n",
    "\n",
    "# solve via iterative rounding\n",
    "sol_ird = ird.approximation_via_iterativeRounding(tree = T, links = L, link_weights = None)\n",
    "\n",
    "# solve via uplinks\n",
    "sol_upl = upl.approximation_via_uplinks(tree = T, root = 0, links = L, link_weights = None)\n",
    "\n",
    "# solve via matching heuristic\n",
    "sol_mat = mat.approximation_via_matchingHeuristic(\n",
    "    tree = T, links = L, matching_procedure = 'max_weight', leaf_nonleaf_selection = 'greedy'\n",
    ")\n",
    "\n",
    "print(sol_mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21291818",
   "metadata": {},
   "source": [
    "We can also retrieve the approximation ratios of the approximation algorithms for a set of samples, e.g. here is the result for the matching heuristic (similar functions are defined for the other approximation algorithms). Note that whenever we run the function, the output is saved in the `saved_outputs` file. Thus, if the cell is run again, the output should appear immediately. Notice that whenever an instance is infeasible, the entry in the approximation ratios array is `nan`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c5122687",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1., nan,  1.,\n",
       "        1.,  1.,  1.,  1.,  1.,  1.,  1.])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat.get_approximation_ratios_of_matchingHeuristic_approximation(\n",
    "    matching_procedure = 'max_weight', \n",
    "    leaf_nonleaf_selection = 'greedy', \n",
    "    samples = 20, \n",
    "    n = 10, \n",
    "    factor = 2, \n",
    "    output_directory = 'saved_outputs'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2982cf5",
   "metadata": {},
   "source": [
    "### Comparing algorithms\n",
    "\n",
    "When we wish to compare a set of algorithms, for a specific TAP instance, we can use the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5ffc94c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>algorithm</th>\n",
       "      <th>value</th>\n",
       "      <th>(1, 7)</th>\n",
       "      <th>(2, 9)</th>\n",
       "      <th>(3, 4)</th>\n",
       "      <th>(0, 9)</th>\n",
       "      <th>(1, 5)</th>\n",
       "      <th>(0, 3)</th>\n",
       "      <th>(0, 6)</th>\n",
       "      <th>(6, 9)</th>\n",
       "      <th>(1, 8)</th>\n",
       "      <th>(4, 7)</th>\n",
       "      <th>(1, 6)</th>\n",
       "      <th>(3, 5)</th>\n",
       "      <th>(0, 2)</th>\n",
       "      <th>(3, 9)</th>\n",
       "      <th>(5, 7)</th>\n",
       "      <th>(8, 9)</th>\n",
       "      <th>(6, 8)</th>\n",
       "      <th>(4, 5)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>natural LP relaxation</td>\n",
       "      <td>2.333333</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>0.333333</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>0.333333</td>\n",
       "      <td></td>\n",
       "      <td>0.666667</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.333333</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>exact</td>\n",
       "      <td>3.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>uplinks</td>\n",
       "      <td>3.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>naive rounding</td>\n",
       "      <td>5.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>iterative rounding</td>\n",
       "      <td>3.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>matching heuristic B</td>\n",
       "      <td>3.000000</td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>matching heuristic WG</td>\n",
       "      <td>3.000000</td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>matching heuristic WM</td>\n",
       "      <td>3.000000</td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>matching heuristic RG</td>\n",
       "      <td>3.000000</td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>matching heuristic RM</td>\n",
       "      <td>3.000000</td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               algorithm     value (1, 7) (2, 9)    (3, 4) (0, 9) (1, 5)  \\\n",
       "0  natural LP relaxation  2.333333                0.333333                 \n",
       "1                  exact  3.000000                                         \n",
       "2                uplinks  3.000000                     1.0    1.0          \n",
       "3         naive rounding  5.000000                     1.0                 \n",
       "4     iterative rounding  3.000000                     1.0                 \n",
       "5   matching heuristic B  3.000000           1.0                           \n",
       "6  matching heuristic WG  3.000000           1.0                           \n",
       "7  matching heuristic WM  3.000000           1.0                           \n",
       "8  matching heuristic RG  3.000000           1.0                           \n",
       "9  matching heuristic RM  3.000000           1.0                           \n",
       "\n",
       "  (0, 3) (0, 6)    (6, 9) (1, 8)    (4, 7) (1, 6) (3, 5) (0, 2)    (3, 9)  \\\n",
       "0                0.333333         0.666667                       0.666667   \n",
       "1                                 1.000000                            1.0   \n",
       "2                                 1.000000                                  \n",
       "3                     1.0         1.000000                            1.0   \n",
       "4                                 1.000000                            1.0   \n",
       "5                                 1.000000                            1.0   \n",
       "6                                 1.000000                            1.0   \n",
       "7                                 1.000000                            1.0   \n",
       "8                                 1.000000                            1.0   \n",
       "9                                 1.000000                            1.0   \n",
       "\n",
       "     (5, 7) (8, 9) (6, 8) (4, 5)  \n",
       "0  0.333333                       \n",
       "1       1.0                       \n",
       "2                                 \n",
       "3       1.0                       \n",
       "4                                 \n",
       "5                                 \n",
       "6                                 \n",
       "7                                 \n",
       "8                                 \n",
       "9                                 "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compare_outputs(\n",
    "    T = T, \n",
    "    links = L, \n",
    "    root = 0, \n",
    "    algorithms_to_compare = ['NLP', 'EXT', 'UPL', 'NRD', 'IRD', 'MAT_B', 'MAT_WG', 'MAT_WM', 'MAT_RG', 'MAT_RM']\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "878d7a8d",
   "metadata": {},
   "source": [
    "We can also immediately output the result if we happen to know the instance details (tree size `n`, size of link set `factor` and random seed `seed`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b924cf10",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>algorithm</th>\n",
       "      <th>value</th>\n",
       "      <th>(2, 9)</th>\n",
       "      <th>(3, 4)</th>\n",
       "      <th>(0, 9)</th>\n",
       "      <th>(6, 9)</th>\n",
       "      <th>(4, 7)</th>\n",
       "      <th>(3, 9)</th>\n",
       "      <th>(5, 7)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>natural LP relaxation</td>\n",
       "      <td>2.333333</td>\n",
       "      <td></td>\n",
       "      <td>0.333333</td>\n",
       "      <td></td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>exact</td>\n",
       "      <td>3.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>uplinks</td>\n",
       "      <td>3.000000</td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>naive rounding</td>\n",
       "      <td>5.000000</td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>iterative rounding</td>\n",
       "      <td>3.000000</td>\n",
       "      <td></td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>matching heuristic B</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>matching heuristic WG</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>matching heuristic WM</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>matching heuristic RG</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>matching heuristic RM</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td></td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               algorithm     value (2, 9)    (3, 4) (0, 9)    (6, 9)  \\\n",
       "0  natural LP relaxation  2.333333         0.333333         0.333333   \n",
       "1                  exact  3.000000                                     \n",
       "2                uplinks  3.000000              1.0    1.0             \n",
       "3         naive rounding  5.000000              1.0              1.0   \n",
       "4     iterative rounding  3.000000              1.0                    \n",
       "5   matching heuristic B  3.000000    1.0                              \n",
       "6  matching heuristic WG  3.000000    1.0                              \n",
       "7  matching heuristic WM  3.000000    1.0                              \n",
       "8  matching heuristic RG  3.000000    1.0                              \n",
       "9  matching heuristic RM  3.000000    1.0                              \n",
       "\n",
       "     (4, 7)    (3, 9)    (5, 7)  \n",
       "0  0.666667  0.666667  0.333333  \n",
       "1  1.000000       1.0       1.0  \n",
       "2  1.000000                      \n",
       "3  1.000000       1.0       1.0  \n",
       "4  1.000000       1.0            \n",
       "5  1.000000       1.0            \n",
       "6  1.000000       1.0            \n",
       "7  1.000000       1.0            \n",
       "8  1.000000       1.0            \n",
       "9  1.000000       1.0            "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve_instance(\n",
    "    n = 10, \n",
    "    factor = 2, \n",
    "    seed = 7, \n",
    "    selected_only = True, \n",
    "    algorithms_to_compare = ['NLP', 'EXT', 'UPL', 'NRD', 'IRD', 'MAT_B', 'MAT_WG', 'MAT_WM', 'MAT_RG', 'MAT_RM']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f8bc892a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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