Partial Max-restricted Path Consistency

Filtering techniques are essential in the search algorithms solving constraint satisfaction problems (CSPs). Arc consistency (AC) is the most often used filtering technique because it cheaply removes some values that cannot belong to any solutions. Comparing with AC, max-Restricted Path Consistency (maxRPC) has a stronger pruning power while it is not suited for use during search because of the prohibitive time cost. Thus, light maxRPC which is the light version of maxRPC was proposed. Comparing with maxRPC, it has a lower time cost and the search algorithm maintaining light maxRPC (MlmaxRPC) can outperform the search algorithm maintaining AC (MAC) on some problems. However, MlmaxRPC suffers from the time waste in the cases that applying a stricter checking standard does not intrigue any value deletion. In order to avoid the time waste in MlmaxRPC, in this paper, partial maxRPC which is a new approximation of maxRPC is proposed. It only applies the stricter checking standard when the value deletion is of high possibility. MpmaxRPC which is the search algorithm maintaining partial maxRPC has a better average performance than MAC and MlmaxRPC.