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We explore a method for computing admissible heuristic evaluation functionsfor search problems. It utilizes pattern databases, which are precomputedtables of the exact cost of solving various subproblems of an existing problem.Unlike standard pattern database heuristics, however, we partition our problemsinto disjoint subproblems, so that the costs of solving the differentsubproblems can be added together without overestimating the cost of solvingthe original problem. Previously, we showed how to statically partition thesliding-tile puzzles into disjoint groups of tiles to compute an admissibleheuristic, using the same partition for each state and problem instance. Herewe extend the method and show that it applies to other domains as well. We alsopresent another method for additive heuristics which we call dynamicallypartitioned pattern databases. Here we partition the problem into disjointsubproblems for each state of the search dynamically. We discuss the pros andcons of each of these methods and apply both methods to three different problemdomains: the sliding-tile puzzles, the 4-peg Towers of Hanoi problem, andfinding an optimal vertex cover of a graph. We find that in some problemdomains, static partitioning is most effective, while in others dynamicpartitioning is a better choice. In each of these problem domains, eitherstatically partitioned or dynamically partitioned pattern database heuristicsare the best known heuristics for the problem.

Additive Pattern Database Heuristics