A pattern database (PDB) is a pre-computed lookup table storing shortest distances from abstract states to abstract goal states. PDBs are key components in heuristic search as their entries are used to prune paths that cannot lead to an optimal solution. With the sliding-tile puzzle as an exemplary application domain, we present methods to improve the precision and size of PDBs by improving additive pattern databases to zero-aware additive pattern databases (ZPDBs), reducing the compression rate from previously 1.6 bit to 1 bit per entry, generating optimal additive pattern partitionings, and building effective collections of pattern databases. With these enhancements, we achieve an overall 8.59-fold performance gain on the 24-puzzle compared to the previously best set of 6-tile PDBs.

The Pancake problem has become a classical combinatorial problem. Different attempts have been made to optimally solve it and/or to derive tighter bounds on the diameter of its state space for a different number of discs. Until very recently, the most successful technique for solving different instances optimally was based on Pattern Databases. Although different approaches have been tried, solutions with Pattern Databases on Pancakes with more than 19 discs have never been reported. In this work, a new technique is introduced which allows the definition of Additive Pattern Databases for solving Pancakes of an arbitrary length. As a result, this technique solves Pancake problems with twice as many discs as the largest ones solved nowadays with other techniques based on Pattern Databases saving up to two orders of magnitude of space.

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