Partition-Based Lower Bound for Max-CSP

Abstract

In this paper we address Max-CSP, a constraint optimization problem typically solved using a branch and bound scheme. It is well known that the efficiency of branch and bound greatly depends on the quality of the available lower bound. Previous approaches aggregate to the lower bound individual contributions of unassigned variables. In this paper, we augment this approach by adding global contributions of disjoint subsets of unassigned variables, which requires a partition of the set of unassigned variables. Using this idea, we introduce the partition-based lower bound. It improves previous approaches based on individual contributions in the sense that our method can be added up to previous bounds, possibly increasing their value. We demonstrate our method presenting two new algorithms, PFC-PRDAC and PFC-MPRDAC, which are the natural successors of PFC-RDAC and PFC-MRDAC augmented with our approach. We provide experimental evidence for the superiority of the new algorithms on random problems and real instances of weighted over-constrained problems.