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For which constraint graphs does arc consistency decide satisfiability?

  • A.Graphs containing exactly one cycle
  • B.Trees
  • C.Complete graphs in which every pair is constrained
  • D.Graphs in which every variable has the same domain

Answer: B

A tree structured problem can be made arc consistent in one sweep from the leaves and then solved without any backtracking at all, in time linear in the number of variables. That is why identifying or creating tree structure is so valuable. Complete graphs are the hardest case, domain uniformity is irrelevant and a single cycle already breaks the guarantee. A structural property that converts an exponential problem into a linear one is worth checking for before any search is attempted.

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