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When may the values from two pattern databases be added?

  • A.When each database is admissible on its own
  • B.When the two subproblems have the same number of states
  • C.When the subproblems involve disjoint sets of moves
  • D.When both databases were built from the same goal state

Answer: C

Addition preserves admissibility only if no move is counted in both databases, which requires the subproblems to partition the moves rather than merely the tiles. Otherwise the sum may exceed the true cost. Shared goals, individual admissibility and equal size are not sufficient. A condition that permits addition rather than merely maximisation is valuable because sums are far larger than maxima, and it is worth the care needed to establish it.

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