april 26

• homework

overview of chapter 12, "coping with limitations"

backtracking algorithms

• idea is to make tree of possible states moving toward solution
• ... but abandon any branches which don't work
• ... or have already been seen (if you're remembering 'em all)
• example: hamiltonian circuit
• example: sudoku
• similar to brute-force, but not *quite* the same: some possibilities are never examined
• can sometimes exploit symmetry to reduce search
• still often exponential time
• Talk about 12.1 #10

branch and bound

• similar
• but another reason for abandoning branch
• namely that its worse than something better
• alpha-beta game-tree pruning is of this variety
• typically requires a numeric "how good is this" for each node
• order that the branches are visited matters: visit best looking (smallest) ones first
• variations on this theme include algorithms that try to invent a "how good is this" function to constrain the search; these functions are called "heuristics"

NP-hard

• various problem-specific heuristics
• ... that try to do the right thing
• example: traveling salesman
  • greedy nearest neighbor search (simple but not great)
  • multifragment-heurstic
  • others to be looked at next week