The approximability of MAX CSP with fixed-value constraints

Deineko, V.; Jonsson, P.; Klasson, M.; Krokhin, A.

Abstract

In the maximum constraint satisfaction problem (MAX CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given finite domain to the variables so as to maximize the number (or the total weight, for the weighted case) of satisfied constraints. This problem is NP-hard in general, and, therefore, it is natural to study how restricting the allowed types of constraints affects the approximability of the problem. In this article, we show that any MAX CSP problem with a finite set of allowed constraint types, which includes all fixed-value constraints (i.e., constraints of the form x = a), is either solvable exactly in polynomial time or else is APX-complete, even if the number of occurrences of variables in instances is bounded. Moreover, we present a simple description of all polynomial-time solvable cases of our problem. This description relies on the well-known algebraic combinatorial property of supermodularity.

Citation

Deineko, V., Jonsson, P., Klasson, M., & Krokhin, A. (2008). The approximability of MAX CSP with fixed-value constraints. Journal of the ACM, 55(4), Article 16. https://doi.org/10.1145/1391289.1391290

• Journal Article Type: Article
• Publication Date: Sep 1, 2008
• Deposit Date: Dec 18, 2009
• Publicly Available Date: Jul 30, 2010
• Journal: Journal of the Association for Computing Machinery.
• Print ISSN: 0004-5411
• Electronic ISSN: 1557-735X
• Publisher: Association for Computing Machinery (ACM)
• Peer Reviewed: Peer Reviewed
• Volume: 55
• Issue: 4
• Article Number: 16
• DOI: https://doi.org/10.1145/1391289.1391290
• Public URL: https://durham-repository.worktribe.com/output/1524270
• Publisher URL: http://portal.acm.org/citation.cfm?doid=1391289.1391290