Dual lookups in pattern databases

A pattern database (PDB) is a heuristic function stored as a lookup table. Symmetries of a state space are often used to enable multiple values to be looked up in a PDB for a given state. This paper introduces an additional PDB lookup, called the dual PDB lookup. A dual PDB lookup is always admissible but can return inconsistent values. The paper also presents an extension of the well-known pathmax method so that inconsistencies in heuristic values are propagated in both directions (child-to-parent, and parent-to-child) in the search tree. Experiments show that the addition of dual lookups and bidirectional pathmax propagation can reduce the number of nodes generated by IDA* by over one order of magnitude in the TopSpin puzzle and Rubik's Cube, and by about a factor of two for the sliding tile puzzles.