A talk with 3 titles By Patrick Prosser

2. A talk with 3 titles By Patrick Prosser

3. Research … how not to do it LDS revisited (aka Chinese whispers) Yet Another Flawed Talk by Patrick Prosser

5. Send reinforcements. We’re going to advance.

7. Send three and fourpence. We’re going to a dance!

8. 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

9. 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

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

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

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

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

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

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

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

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

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

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

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

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

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

23. 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

24. What’s a heuristic?

25. Limited Discrepancy Search (LDS)

27. Motivation for lds

28. Motivation for LDS

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

30. Limited Discrepancy Search (LDS) Ginsberg & Harvey Take no discrepancies (go with the heuristic, go left!)

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

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

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

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

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

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

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

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

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

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

46. Now take 2 discrepancies

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

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

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

50. First proposal For discrepancies 0 to n