Pathfinding Peril - BCS 2014

Finding the shortest path through a connected graph is a complex problem, and one which has a number of very useful applications. Thankfully there are some efficient algorithms out there which solve it well. The first part of the session will take you through some basic theory and how the A-Star algorithm works.
In the second part, you will then put your newly-found pathfinding skills to the test! We'll run a tournament for the remaining hour and a bit, using a robot tournament engine. You'll be able to write a robot in any language, which will be one of two characters in a maze, and the idea is to find the exit as soon as possible without being eaten by the minotaur that roams randomly around it.

Transcript

1. Pathfinding Peril Chris Parsons
2. Huh? What is it all good for... Absolutely nothing?
3. Games
4. Workshop Plan Introduction Graph Theory Pathfinding Algorithms The Maze Contest
5. Graph Theory A B D C E F G
6. What is it all good for... Graphs can model internet networks, data organisation, computation flow, neural networks, the web, wikis, molecular structures, linguistics, social networks, biological habitats, transport networks, etc.
7. Shortest route from B to C A B D C E F G
8. “Brute force” A B D C E F G
9. “Brute force” A B D C E F G
10. “Brute force” A B D C E F G
11. Weighted graphs A B D E F G 3 3 17 2 2 3 22 1 C
12. B - E - C will cost 19 A B D E F G 3 3 17 2 2 3 22 1 C
13. ...but B-A-G-D-C is only 9 A B D E F G 3 3 17 2 2 3 22 1 C
14. Dijkstra's Algorithm Published 1959 Uses an ordered set of open nodes, tracking minimum cost to each
15. Shortest route from B to C A B D E F G 3 3 17 2 2 3 22 1 C
16. Visit B Node Cost B 0 A (from B) 3 F (from B) 3 E (from B) 17 A B D E F G 3 3 17 2 2 3 22 1 C
17. Visit A Node Cost B 0 A (from B) 3 F (from B) 3 G (from A) 6 E (from B) 17 A B D E F G 3 3 17 2 2 3 22 1 C
18. Visit F Node Cost B 0 A (from B) 3 F (from B) 3 G (from A) 6 E (from B) 17 (25 is bigger) A B D E F G 3 3 17 2 2 3 22 1 C
19. Visit G Node Cost B 0 A (from B) 3 F (from B) 3 G (from A) 6 D (from G) 8 E (from B) 17 A B D E F G 3 3 17 2 2 3 22 1 C
20. Visit D Node Cost B 0 A (from B) 3 F (from B) 3 G (from A) 6 D (from G) 8 C (from D) 9 E (from B) 17 A B D E F G 3 3 17 2 2 3 22 1 C
21. Visit C - we’re done! Node Cost B 0 A (from B) 3 F (from B) 3 G (from A) 6 D (from G) 8 C (from D) 9 E (from B) 17 A B D E F G 3 3 17 2 2 3 22 1 C
22. Updated weights A B D E F G 3 3 17 2 2 3 3 1 C
23. Visit B Node Cost B 0 A (from B) 3 F (from B) 3 E (from B) 17 A B D E F G 3 3 17 2 2 3 3 1 C
24. Visit A Node Cost B 0 A (from B) 3 F (from B) 3 G (from A) 6 E (from B) 17 A B D E F G 3 3 17 2 2 3 3 1 C
25. Visit F Node Cost B 0 A (from B) 3 F (from B) 3 G (from A) 6 E (from F) 6 A B D E F G 3 3 17 2 2 3 3 1 C
26. Visit G Node Cost B 0 A (from B) 3 F (from B) 3 G (from A) 6 E (from F) 6 D (from G) 8 A B D E F G 3 3 17 2 2 3 3 1 C
27. Visit E Node Cost B 0 A (from B) 3 F (from B) 3 G (from A) 6 E (from F) 6 C (from E) 8 D (from G) 8 A B D E F G 3 3 17 2 2 3 3 1 C
28. Visit C - we’re done! Node Cost B 0 A (from B) 3 F (from B) 3 G (from A) 6 E (from F) 6 C (from E) 8 D (from G) 8 A B D E F G 3 3 17 2 2 3 3 1 C
29. A*
    algorithm Published 1968 Variation on Dijkstra, using a heuristic to cut down on nodes to visit
30. Distance Heuristic A 23 B 10 D 12 E 13 F 18 G 20 3 3 17 2 2 3 22 1 C 0
31. Visit B Node Cost Order B 0 10 (0+10) F 3 21 (3+18) A 3 26 (3+23) E 17 40 (17+13) A 23 B 10 D 12 E 13 F 18 G 20 3 3 17 2 2 3 22 1 C 0
32. Visit F Node Cost Order B 0 10 (0+10) F 3 21 (3+18) A 3 26 (3+23) E 17 30 (17+13) A 23 B 10 D 12 E 13 F 18 G 20 3 3 17 2 2 3 22 1 C 0
33. Visit A Node Cost Order B 0 10 (0+10) F 3 21 (3+18) A 3 26 (3+23) G 6 26 (6+20) E 17 30 (17+13) A 23 B 10 D 12 E 13 F 18 G 20 3 3 17 2 2 3 22 1 C 0
34. Visit G Node Cost Order B 0 10 (0+10) F 3 21 (3+18) A 3 26 (3+23) G 6 26 (6+20) D 8 20 (8+12) E 17 30 (17+13) A 23 B 10 D 12 E 13 F 18 G 20 3 3 17 2 2 3 22 1 C 0
35. Visit D Node Cost Order B 0 10 (0+10) F 3 21 (3+18) A 3 26 (3+23) G 6 26 (6+20) D 8 20 (8+12) C 9 9 (9 +0) E 17 30 (17+13) A 23 B 10 D 12 E 13 F 18 G 20 3 3 17 2 2 3 22 1 C 0
36. Visit C - we’re done! Node Cost Order B 0 10 (0+10) F 3 21 (3+18) A 3 26 (3+23) G 6 26 (6+20) D 8 20 (8+12) C 9 9 (9 +0) E 17 30 (17+13) A 23 B 10 D 12 E 13 F 18 G 20 3 3 17 2 2 3 22 1 C 0
37. Non-admissible Heuristic A 23 B 10 D 12 E 13 F 18 G 20 3 3 17 2 2 3 22 1 C 0
38. Different Heuristics Dijkstra no heuristic A* exact distance (admissible) http://en.wikipedia.org/wiki/A*_search_algorithm http://en.wikipedia.org/wiki/Dijkstra%27s_algorithm A* over-egging distance (non-admissible)
39. Summary Brute force approach: O(n²) (ouch!) Dijkstra: guarantees best path but still can be slow A*: depending on Heuristic can trade speed for best path Admissible Heuristics (never overestimating cost) is the sweet spot for A*
40. Your turn Wifi: BCS Guest Password: *** Visit http://10.30.22.75:3000 for the tournament The rules for the game are shown Rest of this session for practice (1m rounds) Proper contest will be 5m rounds after the break
41. Slides + tournament online https://speakerdeck.com/u/chrismdp/p/pathfinding-peril http://github.com/chrismdp/robot_tournament
42. Sol Trader I’m a web programmer moved back into Games Running a Sol Trader Kickstarter this month http://soltrader.net
43. Thanks! Chris Parsons @chrismdp - http://pa.rsons.org Sol Trader @soltdr - http://soltrader.net