Histogram Arc Consistency as a Value Ordering Heuristic

Abstract

The Constraint Satisfaction Problem (CSP) is NP-hard. Finding solutions requires searching in an exponential space of possible variable assignments. Good value ordering heuristics are essential for finding solutions to CSPs. Such heuristics estimate the marginal probability that any particular variable assignment will appear in a globally consistent solution. Unfortunately, computing such solution probabilities exactly is also NP-hard. Thus estimation algorithms are required. Previous results have been very encouraging but computationally expensive. In this paper, we present two new algorithms, called Histogram Arc Consistency (HAC) and μ Arc Consistency(μAC), which generate fast estimates of solution probabilities during constraint propagation. This information is used as value ordering heuristics to guide backtrack search. Our experimental results on random CSPs show that these methods indeed provide significant heuristic guidance compared to previous methods while remaining efficient to compute.