Substituabilité au voisinage pour le cadre WCSP

WCSP is an optimization problem for which many forms of soft local (arc) consistencies such as existential directional arc consistency (EDAC) and virtual arc consistency (VAC) have been proposed these last years. 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 is based on the concept of overcost of 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 optimized algorithm and we show on various series of WCSP instances, the practical interest of maintaining pcost together with AC*, FDAC or EDAC, during search.