Partial lazy forward checking

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.Postprint (published version

Using Mean Field Methods for Boosting Backtrack Search in Constraint Satisfaction Problems

Exact and inexact methods can be used for solving Constraint Satisfaction Problems (CSP), i.e. for finding a variable assignment which violates none of the constraints or minimizes the number of violated constraints. Based on a Backtrack tree search, exact methods are able to produce an optimal assignment, when no time limit is imposed. Based on local improvement mechanisms, inexact methods cannot guarantee that, but may produce better quality assignments in a limited time. In this paper, we show how an inexact method, coming from statistical physics, and more precisely from the Mean Field Theory, can boost an exact method by providing it with a good quality assignment, whose valuation can be used as an initial upper bound, and with two heuristics for ordering variables and values. Experiments on randomly generated classical and partial CSPs show significative gains in terms of time, even when adding the times used by both the Mean Field and the Backtrack methods