A Comparison of h ² and MMM for Mutex Pair Detection Applied to Pattern Databases

Abstract

In state space search or planning, a pair of variable-value assignments that does not occur in any reachable state is considered a mutually exclusive (mutex) pair. To improve the efficiency of planners, the problem of detecting such pairs has been addressed frequently in the planning literature. No known efficient method for detecting mutex pairs is able to find all such pairs. Hence, the number and type of mutex constraints detected by various algorithms are different from one another.

The purpose of this paper is to study the effects on search performance when errors are made by the mutex detection method that is informing the construction of a pattern database (PDB). PDBs are deployed for creating heuristic functions that are then used to guide search. We consider two mutex detection methods, h ², which can fail to recognize a mutex pair but never regards a reachable pair as mutex, and the sampling-based method MMM, which makes the opposite type of error. Both methods are very often perfect, i.e. they exactly identify which pairs are mutex and which are reachable. In the cases that they err that we examine in this paper, h ²’s errors cause search to be moderately slower (7% −24%) whereas MMM’s errors have very little effect on search speed or suboptimality, even when its sample size is quite small.