Interleaving Levels of Consistency Enforcement for Singleton Arc Consistency in CSPs, with a New Best (N)SAC Algorithm

Abstract

A basic technique used in algorithms for constraint satisfaction problems (CSPs) is removing values that are locally inconsistent, since they cannot form part of a globally consistent solution. The best-known algorithms of this type establish arc consistency (AC), where every value has support in neighbouring domains. Here, we consider algorithms that use AC repeatedly under severe local assumptions to achieve higher overall levels of consistency. These algorithms establish (neighbourhood) singleton arc consistency ((N)SAC). Most of these use simple AC interleaved with the basic (N)SAC procedure. To date, however, this strategy of interleaving weaker and stronger forms of reasoning has not received much attention in and of itself. Moreover, one of the best (N)SAC algorithms (called (N)SACQ) does not use this method. This paper investigates the effects of interleaving and presents new methods based on this idea. We show that different kinds of problems vary greatly in their amenability to AC interleaving; while in most cases it is beneficial, with some algorithms and problem types it can be harmful. More significantly, when this feature is added to (N)SACQ algorithms, the latter’s superiority to other (N)SAC algorithms becomes more consistent and decisive. We also consider an AC-4 based approach to interleaving as well as interleaving with stronger methods than AC.