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
   

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2. Huh? What is it
   all good for...
   Absolutely nothing?
   

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3. Games
   

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4. Workshop Plan
   Introduction
   Graph Theory
   Pathfinding Algorithms
   The Maze Contest
   

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5. Graph Theory
   A
   B
   D
   C
   E
   F
   G
   

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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.
   

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7. Shortest route from B to C
   A
   B
   D
   C
   E
   F
   G
   

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8. “Brute force”
   A
   B
   D
   C
   E
   F
   G
   

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9. “Brute force”
   A
   B
   D
   C
   E
   F
   G
   

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10. “Brute force”
    A
    B
    D
    C
    E
    F
    G
    

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11. Weighted graphs
    A
    B
    D
    E
    F
    G
    3
    3 17
    2
    2
    3
    22
    1
    C
    

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12. B - E - C will cost 19
    A
    B
    D
    E
    F
    G
    3
    3 17
    2
    2
    3
    22
    1
    C
    

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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
    

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14. Dijkstra's
    Algorithm
    Published 1959
    Uses an ordered set of
    open nodes, tracking
    minimum cost to each
    

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15. Shortest route from B to C
    A
    B
    D
    E
    F
    G
    3
    3 17
    2
    2
    3
    22
    1
    C
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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22. Updated weights
    A
    B
    D
    E
    F
    G
    3
    3 17
    2
    2
    3
    3
    1
    C
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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29. A*
    algorithm
    Published 1968
    Variation on Dijkstra, using a
    heuristic to cut down on
    nodes to visit
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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)
    

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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*
    

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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
    

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41. Slides + tournament online
    https://speakerdeck.com/u/chrismdp/p/pathfinding-peril
    http://github.com/chrismdp/robot_tournament
    

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42. Sol Trader
    I’m a web programmer moved back into Games
    Running a Sol Trader Kickstarter this month
    http://soltrader.net
    

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43. Thanks!
    Chris Parsons
    @chrismdp - http://pa.rsons.org
    Sol Trader
    @soltdr - http://soltrader.net
    

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