Lecture 3: Realistic Search Algorithms

• Ginsberg ch. 4

Notes

• NP-Completeness Revisited
  • Proof technique: show that
    • Problem is in NP (easy).
    • Problem is as hard as an NP-complete problem (hard).
  • Usually show NP-hardness by many-one reduction: show that every instance of some NP-complete problem A could be solved by converting it (in polytime) to an instance of the target problem B and solving that. We say that we reduce A to B, and write A<=B.
  • Polytime transformation is important (e.g., SAT is not in P)
  • Transformations
    • Restriction: the easy way.
    • Local replacement: simple instance isomorphism.
    • Component design: complicated instance construction.
• Search Algorithms
  • Blind search revisited
    • Iterative deepening: (b+1)/(b-1)
    • Iterative broadening: 1 or b/d
    • Iterative sampling: d (binary case)
    • Accepting constant factors.
    • Optimization via ``branch-and-bound''.
  • Heuristically-guided search
    • The idea: where heuristic values come from.
    • Cost/benefit in heuristic values.
    • Local search using heuristics
      • Local minima
      • Tabu
      • Noise
    • Systematic search using heuristics
      • Heuristic DFS and heuristic errors
      • A* search and heuristic admissibility
      • LDS and accepting constant factors
      • Other algorithms
  • Applications
    • Blocks-world
    • Scheduling
    • General constraint satisfaction
• Some comments on the DDJ problem