Partial lazy forward checking

Abstract

Partial forward checking (PFC) may perform more consistency checks than really needed to detect dead-ends in MAX-CSP. After analyzing PFC, we have identified four causes of redundant check computation: (a) unnecessary lookahead when detecting an empty domain, (b) not always using the better bounds for future value pruning, (c) computing in advance inconsistency counts, and (d) lookahead is performed on the whole set of future variables. We present the partial lazy forward checking (PLFC) algorithm, which follows a lazy approach delaying as much as possible inconsistency count computation, keeping updated the contribution of future variables to the lower bound. This algorithm avoids the causes of redundant checks identified for PFC. It can be easily combined with DACs, producing the PLFC-DAC algorithm. Empirical results on random problems show that PLFC-DAC outperforms previous algorithms in both consistency checks and CPU time.