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A talk with 3 titles By Patrick Prosser

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A talk with 3 titles By Patrick Prosser

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  1. A talk with 3 titles By Patrick Prosser

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

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

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

  5. 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

  6. 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

  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 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 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. 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. 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

  21. What’s a heuristic?

  22. Limited Discrepancy Search (LDS)

  23. Motivation for lds

  24. Motivation for LDS

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

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

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

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

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

  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. 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. Now take 2 discrepancies

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

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

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

  46. First proposal For discrepancies 0 to n