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Research how not to do it

Research how not to do it. Quick Intro. A refresher Chronological Backtracking (BT) what’s that then? when/why do we need it?. Limited Discrepancy Search (lds) what’s that then. Then the story … how not to do it. An example problem (to show chronological backtracking (BT)). 1. 2.

Research how not to do it

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Presentation Transcript

1. Research how not to do it

2. Quick Intro • A refresher • Chronological Backtracking (BT) • what’s that then? • when/why do we need it? • Limited Discrepancy Search (lds) • what’s that then Then the story … how not to do it

3. An example problem (to show chronological backtracking (BT)) 1 2 3 4 5 Colour each of the 5 nodes, such that if they are adjacent, they take different colours

4. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 v1 v2 v3 v4 v5 4 5

5. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 v1 v2 v3 v4 v5 4 5

6. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 v1 v2 v3 v4 v5 4 5

7. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 v1 v2 v3 v4 v5 4 5

8. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 v1 v2 v3 v4 v5 4 5

9. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 v1 v2 v3 v4 v5 4 5

10. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 5 4 v1 v2 v3 v4 v5

11. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 5 4 v1 v2 v3 v4 v5

12. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 5 4 v1 v2 v3 v4 v5

13. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 5 4 v1 v2 v3 v4 v5

14. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 5 4 v1 v2 v3 v4 v5

15. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 5 4 v1 v2 v3 v4 v5

16. A Tree Trace of BT (assume domain ordered {R,B,G}) 1 2 3 5 4 v1 v2 v3 v4 v5

17. An inferencing step A heuristic (Brelaz) Could do better • Improvements: • when colouring a vertex with colour X • remove X from the palette of adjacent vertices • when selecting a vertex to colour • choose the vertex with the smallest palette • tie break on adjacency with uncoloured vertices Conjecture: our heuristic is more reliable as we get deeper in search

18. What’s a heuristic?

19. Limited Discrepancy Search (LDS)

20. Motivation for lds

21. Motivation for LDS

22. Limited Discrepancy Search • LDS • show the search process • assume binary branching • assume we have 4 variables only • assume variables have 2 values each

23. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take no discrepancies (go with the heuristic)

24. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take no discrepancies

25. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take no discrepancies

26. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take no discrepancies

27. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 1 discrepancy

28. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 1 discrepancy

29. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 1 discrepancy

30. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 1 discrepancy

31. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 1 discrepancy

32. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 1 discrepancy

33. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 1 discrepancy

34. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 1 discrepancy

35. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 1 discrepancy

36. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 1 discrepancy

37. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 1 discrepancy

38. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 1 discrepancy

39. Now take 2 discrepancies

40. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 2 discrepancies

41. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 2 discrepancies

42. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take 2 discrepancies

43. First proposal For discrepancies 0 to n

44. k is remaining discrepancies First proposal For discrepancies 0 to n

45. k is remaining discrepancies First proposal Go with heuristic For discrepancies 0 to n

46. k is remaining discrepancies First proposal Go with heuristic Go against then go with For discrepancies 0 to n

47. The lds search process: how it goes (a cartoon)

48. The lds search process: how it goes NOTE: lds revisits search states with k discrepancies When searching with > k discrepancies

49. My pseudo code

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