WCSP integration of soft neighborhood substitutability

Abstract

WCSP is an optimization problem for which many forms of soft local (arc) consistencies have been proposed such as, for example, existential directional arc consistency (EDAC) and virtual arc consistency (VAC). In this paper, we adopt a different perspective by revisiting the well-known property of (soft) substitutability. First, we provide a clear picture of the relationships existing between soft neighborhood substitutability (SNS) and a tractable property called pcost which allows us to compare the cost of two values (through the use of so-called cost pairs). We prove that under certain assumptions, pcost is equivalent to SNS but weaker than SNS in the general case since we show that SNS is coNP-hard. We also show that SNS preserves the property VAC but not the property EDAC. Finally, we introduce an algorithm to enforce pcost that benefits from several optimizations (early breaks, residues, timestamping). The practical interest of maintaining pcost together with AC*, FDAC or EDAC, during search. is shown on various series of WCSP instances. © 2012 Springer-Verlag.