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Appendix

The tables below list the non-normalized average path length and runtime results for all 200 variations of path planning methods tested on the Dragon Age: Origins benchmark set. The path lengths are in grid spacings and the runtimes are in microseconds. Tests were run on a 2.7GHz Intel Core i7 laptop with 16GB of RAM, the same machine used by Goldstein et al. (2022). For the heuristic search methods, the absolute shortest possible average length is 185.778246.

A* Search

Neighborhood Search Method Smoothing Path Length Runtime
4 Regular A* Search Greedy 193.365718 534.387950
8 Regular A* Search Greedy 187.589861 826.688916
16 Regular A* Search Greedy 186.271375 1626.100770
32 Regular A* Search Greedy 185.984016 2881.977007
64 Regular A* Search Greedy 185.879095 4973.799355
4 Central A* Search Greedy 186.671385 1217.876808
8 Central A* Search Greedy 185.986902 1197.944923
16 Central A* Search Greedy 185.847056 1989.447834
32 Central A* Search Greedy 185.807597 3275.682891
64 Central A* Search Greedy 185.792561 5494.900880
4 Regular A* Search Tentpole 191.092794 546.832701
8 Regular A* Search Tentpole 186.628553 847.940695
16 Regular A* Search Tentpole 185.959140 1636.882757
32 Regular A* Search Tentpole 185.840904 2878.747123
64 Regular A* Search Tentpole 185.801373 4967.486637
4 Central A* Search Tentpole 185.974571 1293.145968
8 Central A* Search Tentpole 185.819156 1247.897377
16 Central A* Search Tentpole 185.793087 2008.612702
32 Central A* Search Tentpole 185.784785 3302.039216
64 Central A* Search Tentpole 185.779853 5551.712036

Jump Point Search (JPS)

Neighborhood Search Method Smoothing Path Length Runtime
4 Regular JPS Greedy 201.039027 408.654190
8 Regular JPS Greedy 188.477175 321.472344
16 Regular JPS Greedy 186.243174 627.678783
32 Regular JPS Greedy 185.918231 1180.227494
64 Regular JPS Greedy 185.833812 2425.068509
4 Central JPS Greedy 186.671385 1084.345122
8 Central JPS Greedy 185.986902 697.907750
16 Central JPS Greedy 185.847056 933.688681
32 Central JPS Greedy 185.807597 1517.915286
64 Central JPS Greedy 185.792561 2786.210819
4 Regular JPS Tentpole 197.096915 418.021204
8 Regular JPS Tentpole 187.170755 327.009705
16 Regular JPS Tentpole 186.038859 634.523693
32 Regular JPS Tentpole 185.863202 1180.834018
64 Regular JPS Tentpole 185.810860 2419.373892
4 Central JPS Tentpole 185.974571 1106.927825
8 Central JPS Tentpole 185.819156 702.821126
16 Central JPS Tentpole 185.793087 923.437070
32 Central JPS Tentpole 185.784785 1472.852775
64 Central JPS Tentpole 185.779853 2802.757366

Bounded Jump Point Search

Neighborhood Search Method Smoothing Path Length Runtime
4 Regular Bounded JPS Greedy 200.433325 347.863703
8 Regular Bounded JPS Greedy 188.430357 286.518214
16 Regular Bounded JPS Greedy 186.237935 526.341604
32 Regular Bounded JPS Greedy 185.916391 973.875580
64 Regular Bounded JPS Greedy 185.833489 1956.143089
4 Central Bounded JPS Greedy 186.671385 1021.085621
8 Central Bounded JPS Greedy 185.986902 693.019877
16 Central Bounded JPS Greedy 185.847056 814.974841
32 Central Bounded JPS Greedy 185.807597 1245.191221
64 Central Bounded JPS Greedy 185.792561 2293.949523
4 Regular Bounded JPS Tentpole 196.551539 358.722630
8 Regular Bounded JPS Tentpole 187.140066 293.213547
16 Regular Bounded JPS Tentpole 186.035377 530.480487
32 Regular Bounded JPS Tentpole 185.862085 968.245246
64 Regular Bounded JPS Tentpole 185.810589 1960.168195
4 Central Bounded JPS Tentpole 185.974571 1027.304275
8 Central Bounded JPS Tentpole 185.819156 663.766774
16 Central Bounded JPS Tentpole 185.793087 815.973386
32 Central Bounded JPS Tentpole 185.784785 1250.654212
64 Central Bounded JPS Tentpole 185.779853 2339.332641

Mixed A* Search

Neighborhood Search Method Smoothing Path Length Runtime
4 Regular Mixed A* Search Greedy 191.597298 914.615398
8 Regular Mixed A* Search Greedy 187.961801 1192.996757
16 Regular Mixed A* Search Greedy 186.429905 2681.311567
32 Regular Mixed A* Search Greedy 186.021187 4695.020902
64 Regular Mixed A* Search Greedy 185.889545 8335.502693
4 Central Mixed A* Search Greedy 186.671385 1655.436572
8 Central Mixed A* Search Greedy 185.986902 1610.217601
16 Central Mixed A* Search Greedy 185.847056 3071.352716
32 Central Mixed A* Search Greedy 185.807597 5216.238722
64 Central Mixed A* Search Greedy 185.792561 9029.816636
4 Regular Mixed A* Search Tentpole 189.139226 929.717603
8 Regular Mixed A* Search Tentpole 186.732358 1197.940252
16 Regular Mixed A* Search Tentpole 185.984840 2687.409610
32 Regular Mixed A* Search Tentpole 185.842622 4719.345070
64 Regular Mixed A* Search Tentpole 185.801543 8390.656742
4 Central Mixed A* Search Tentpole 185.974571 1628.300374
8 Central Mixed A* Search Tentpole 185.819156 1619.197273
16 Central Mixed A* Search Tentpole 185.793087 3130.666958
32 Central Mixed A* Search Tentpole 185.784785 5204.472437
64 Central Mixed A* Search Tentpole 185.779853 9104.802187

Mixed Jump Point Search

Neighborhood Search Method Smoothing Path Length Runtime
4 Regular Mixed JPS Greedy 200.396710 413.707733
8 Regular Mixed JPS Greedy 188.423878 377.340498
16 Regular Mixed JPS Greedy 186.242714 774.322450
32 Regular Mixed JPS Greedy 185.916234 1352.991110
64 Regular Mixed JPS Greedy 185.833216 2669.136886
4 Central Mixed JPS Greedy 186.671385 1108.899596
8 Central Mixed JPS Greedy 185.986902 765.950713
16 Central Mixed JPS Greedy 185.847056 1073.335710
32 Central Mixed JPS Greedy 185.807597 1649.392664
64 Central Mixed JPS Greedy 185.792561 3060.202022
4 Regular Mixed JPS Tentpole 196.558070 423.913765
8 Regular Mixed JPS Tentpole 187.128776 383.347960
16 Regular Mixed JPS Tentpole 186.037636 783.730371
32 Regular Mixed JPS Tentpole 185.861571 1353.814327
64 Regular Mixed JPS Tentpole 185.810542 2669.384104
4 Central Mixed JPS Tentpole 185.974571 1094.356620
8 Central Mixed JPS Tentpole 185.819156 755.812120
16 Central Mixed JPS Tentpole 185.793087 1081.203811
32 Central Mixed JPS Tentpole 185.784785 1658.353979
64 Central Mixed JPS Tentpole 185.779853 3047.275998

Dijkstra Search

Neighborhood Search Method Smoothing Path Length Runtime
4 Regular Dijkstra Search Greedy 157.251873 83.935235
8 Regular Dijkstra Search Greedy 154.188250 97.630645
16 Regular Dijkstra Search Greedy 152.511089 184.842748
32 Regular Dijkstra Search Greedy 152.116603 348.246898
64 Regular Dijkstra Search Greedy 151.992054 649.513103
4 Central Dijkstra Search Greedy 152.612682 603.239848
8 Central Dijkstra Search Greedy 152.055011 387.013216
16 Central Dijkstra Search Greedy 151.945177 391.497509
32 Central Dijkstra Search Greedy 151.914072 537.626518
64 Central Dijkstra Search Greedy 151.902037 832.434908
4 Regular Dijkstra Search Tentpole 155.144687 94.182410
8 Regular Dijkstra Search Tentpole 152.982804 105.024445
16 Regular Dijkstra Search Tentpole 152.091715 189.579379
32 Regular Dijkstra Search Tentpole 151.951272 351.292129
64 Regular Dijkstra Search Tentpole 151.912229 644.473922
4 Central Dijkstra Search Tentpole 152.045678 606.499334
8 Central Dijkstra Search Tentpole 151.919454 386.555890
16 Central Dijkstra Search Tentpole 151.901590 407.713721
32 Central Dijkstra Search Tentpole 151.895579 531.521951
64 Central Dijkstra Search Tentpole 151.891721 833.537815

Canonical Dijkstra Search (CDS)

Neighborhood Search Method Smoothing Path Length Runtime
4 Regular CDS Greedy 163.785354 49.419697
8 Regular CDS Greedy 154.021722 40.695473
16 Regular CDS Greedy 152.263140 67.386703
32 Regular CDS Greedy 151.999688 133.528896
64 Regular CDS Greedy 151.934463 282.740716
4 Central CDS Greedy 152.612682 568.013680
8 Central CDS Greedy 152.055011 327.128106
16 Central CDS Greedy 151.945177 270.731337
32 Central CDS Greedy 151.914072 311.776342
64 Central CDS Greedy 151.902037 481.571763
4 Regular CDS Tentpole 160.698606 62.099451
8 Regular CDS Tentpole 152.982259 45.466031
16 Regular CDS Tentpole 152.096336 69.221868
32 Regular CDS Tentpole 151.956872 135.285486
64 Regular CDS Tentpole 151.916566 284.632733
4 Central CDS Tentpole 152.045678 569.287323
8 Central CDS Tentpole 151.919454 326.639556
16 Central CDS Tentpole 151.901590 270.704879
32 Central CDS Tentpole 151.895579 319.175782
64 Central CDS Tentpole 151.891721 488.185994

Bounded Canonical Dijkstra Search

Neighborhood Search Method Smoothing Path Length Runtime
4 Regular Bounded CDS Greedy 163.734843 53.116133
8 Regular Bounded CDS Greedy 153.997510 45.630085
16 Regular Bounded CDS Greedy 152.255571 71.991570
32 Regular Bounded CDS Greedy 151.997883 138.643241
64 Regular Bounded CDS Greedy 151.933452 288.416628
4 Central Bounded CDS Greedy 152.612682 575.341513
8 Central Bounded CDS Greedy 152.055011 332.383648
16 Central Bounded CDS Greedy 151.945177 276.129461
32 Central Bounded CDS Greedy 151.914072 317.685700
64 Central Bounded CDS Greedy 151.902037 478.414886
4 Regular Bounded CDS Tentpole 160.645438 61.299084
8 Regular Bounded CDS Tentpole 152.961026 50.510666
16 Regular Bounded CDS Tentpole 152.091280 74.255481
32 Regular Bounded CDS Tentpole 151.955915 139.588242
64 Regular Bounded CDS Tentpole 151.915896 289.984725
4 Central Bounded CDS Tentpole 152.045678 574.648894
8 Central Bounded CDS Tentpole 151.919454 333.728516
16 Central Bounded CDS Tentpole 151.901590 276.993713
32 Central Bounded CDS Tentpole 151.895579 318.847111
64 Central Bounded CDS Tentpole 151.891721 480.248572

Mixed Dijkstra Search

Neighborhood Search Method Smoothing Path Length Runtime
4 Regular Mixed Dijkstra Search Greedy 156.693050 129.041187
8 Regular Mixed Dijkstra Search Greedy 154.187286 157.753866
16 Regular Mixed Dijkstra Search Greedy 152.510867 326.545713
32 Regular Mixed Dijkstra Search Greedy 152.116534 583.580117
64 Regular Mixed Dijkstra Search Greedy 151.992024 1075.996507
4 Central Mixed Dijkstra Search Greedy 152.612682 646.726533
8 Central Mixed Dijkstra Search Greedy 152.055011 453.257861
16 Central Mixed Dijkstra Search Greedy 151.945177 533.009315
32 Central Mixed Dijkstra Search Greedy 151.914072 766.801755
64 Central Mixed Dijkstra Search Greedy 151.902037 1257.514665
4 Regular Mixed Dijkstra Search Tentpole 154.581298 137.759488
8 Regular Mixed Dijkstra Search Tentpole 152.982715 166.405091
16 Regular Mixed Dijkstra Search Tentpole 152.091707 332.616671
32 Regular Mixed Dijkstra Search Tentpole 151.951266 586.751369
64 Regular Mixed Dijkstra Search Tentpole 151.912223 1073.546127
4 Central Mixed Dijkstra Search Tentpole 152.045678 660.254336
8 Central Mixed Dijkstra Search Tentpole 151.919454 448.443992
16 Central Mixed Dijkstra Search Tentpole 151.901590 532.594152
32 Central Mixed Dijkstra Search Tentpole 151.895579 766.372283
64 Central Mixed Dijkstra Search Tentpole 151.891721 1267.957524

Mixed Canonical Dijkstra Search

Neighborhood Search Method Smoothing Path Length Runtime
4 Regular Mixed CDS Greedy 163.687226 60.396260
8 Regular Mixed CDS Greedy 153.996164 54.694633
16 Regular Mixed CDS Greedy 152.261676 86.865039
32 Regular Mixed CDS Greedy 151.997833 167.970011
64 Regular Mixed CDS Greedy 151.933743 357.694420
4 Central Mixed CDS Greedy 152.612682 586.939997
8 Central Mixed CDS Greedy 152.055011 341.734454
16 Central Mixed CDS Greedy 151.945177 289.804511
32 Central Mixed CDS Greedy 151.914072 345.511306
64 Central Mixed CDS Greedy 151.902037 549.027167
4 Regular Mixed CDS Tentpole 160.605347 68.535977
8 Regular Mixed CDS Tentpole 152.966280 59.410840
16 Regular Mixed CDS Tentpole 152.095247 88.370204
32 Regular Mixed CDS Tentpole 151.955045 168.158011
64 Regular Mixed CDS Tentpole 151.916153 357.132278
4 Central Mixed CDS Tentpole 152.045678 582.268455
8 Central Mixed CDS Tentpole 151.919454 341.649351
16 Central Mixed CDS Tentpole 151.901590 290.972385
32 Central Mixed CDS Tentpole 151.895579 348.633828
64 Central Mixed CDS Tentpole 151.891721 548.413355

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