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Limited Discrepancy Search (LDS): A Heuristic Approach for Chronological Backtracking Problems

Explore the Limited Discrepancy Search method for efficient problem-solving through a heuristic approach. This research delves into the process, implications, and advantages of applying LDS in the context of Chronological Backtracking (BT). Discover how this approach enhances decision-making and reduces search complexities in problem-solving scenarios.

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Limited Discrepancy Search (LDS): A Heuristic Approach for Chronological Backtracking Problems

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  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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