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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.

A domain-independent heuristic function created by an abstraction is usually implemented using a Pattern Database (PDB), which is a lookup table of (abstract state, heuristic value) pairs. PDBs containing high quality heuristic values generally require substantial memory space and therefore need to be compressed. In this paper, we introduce Acyclic Random Hypergraph Compression (ARHC), a domain-independent approach to compressing PDBs using acyclic random r-partite runiform hypergraphs. The ARHC algorithm, which comes in Base and Extended versions, provides fast lookup and a high compression rate. ARHCExtended achieves higher quality heuristics than ARHC-Base by decreasing the heuristic information loss at the cost of some decrease in the compression rate. ARHC shows higher performance than level-by-level Bloom filter PDB compression in all experiments conducted so far.

A popular way to create domain-independent heuristic functions is by using abstraction, where an abstract (coarse) version of the state space is derived from the original state space. An abstraction-based heuristic is usually implemented using a pattern database, a lookup table of (abstract state, heuristic value) pairs. Efficient representation and compression of pattern databases has been the topic of substantial ongoing research. In this paper, we present a novel domain-independent algorithm for this purpose using acyclic r-partite random hypergraphs. The theoretical and experimental results show that our proposed algorithm provides a consistent representation that works well across planning problem domains and provides a good trade-off between space usage and lookup time. Thus, it is suitable to be a standard efficient representation for pattern databases and a benchmark method for other pattern database representation/compression methods.

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