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The approximability of MAX CSP with fixed-value constraints

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

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Authors

V. Deineko

P. Jonsson

M. Klasson



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 Mar 29, 2024
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
Publisher URL http://portal.acm.org/citation.cfm?doid=1391289.1391290

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Copyright Statement
© ACM 2008. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Journal of the ACM,
{The approximability of MAX CSP with fixed-value constraints, 2008}, http://dx.doi.org/10.1145/1391289.1391290





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