Filtering Nogoods Lazily in Dynamic Symmetry Breaking During Search

Abstract

The generation and GAC enforcement of a large number of weak nogoods in Symmetry Breaking During Search (SBDS) is costly and often not worthwhile in terms of prunings. In this paper, we propose weak-nogood consistency (WNC) for nogoods and a lazy propagator for SBDS (and its variants) using watched literal technology. We give formal results on the strength and relatively low space and time complexities of the lazy propagator. Nogoods collected for each symmetry are increasing. We further define generalized weak-incNGs consistency (GWIC) for a conjunction of increasing nogoods, and give a lazy propagator for the incNGs global constraint. We prove GWIC on a conjunction is equivalent to WNC on individual nogoods, and give the space and time complexities. Various lazy versions of SBDS and its variants are implemented. We give experimentation to demonstrate the efficiency of the lazy versions as compared to state of the art symmetry breaking methods.