An examination of probabilistic value-ordering heuristics

Abstract

Searching for solutions to constraint satisfaction problems (CSPs) is NP-haxd in general. Heuristics for variable and value ordering have proven usefiil in guiding the sestrch towards more fruitful areas of the search space and hence reducing the amount of time spent searching for solutions. Static ordering methods impart an ordering in advance of the search and dynamic ordering methods use information about the state of the search to order veJues or variables during the search. A well-known static value ordering heuristic guides the search by ordering values based on an estimate of the number of solutions to the problem. This paper compares the performance of several such heuristics and shows that they do not give a significant improvement to a random ordering for haurd CSPs. We give a dynamic ordering heuristic which decomposes the CSP into speinning trees and uses Bayesian networks to compute probabUistic approximations based on the current search state. Our empirical results show that this dynamic value ordering heuristic is an improvement for sparsely constrained CSPs and detects insoluble problem instances with fewer backtracks in many cases. However, as the problem density increases, our results show that the dynamic method and static methods do not significantly improve search performance.