Dead-End Elimination for Weighted CSP

Abstract

Soft neighborhood substitutability (SNS) is a powerful technique to automatically detect and prune dominated solutions in combinatorial optimization. Recently, it has been shown in [26] that enforcing partial SNS (PSNS^r) during search can be worthwhile in the context of Weighted Constraint Satisfaction Problems (WCSP). However, for some problems, especially with large domains, PSNS^r is still too costly to enforce due to its worst-case time complexity in O(ned ⁴) for binary WCSP. We present a simplified dominance breaking constraint, called restricted dead-end elimination (DEE^r), the worst-case time complexity of which is in O(ned ²). Dead-end elimination was introduced in the context of computational biology as a preprocessing technique to reduce the search space [13, 14, 16, 17, 28, 30]. Our restriction involves testing only one pair of values per variable instead of all the pairs, with the possibility to prune several values at the same time. We further improve the original dead-end elimination criterion, keeping the same time and space complexity as DEE^r. Our results show that maintaining DEE^r during a depth-first branch and bound (DFBB) search is often faster than maintaining PSNS^r and always faster than or similar to DFBB alone.