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The approximability of MAX CSP with fixed-value constraints.

Deineko, V. and Jonsson, P. and Klasson, M. and Krokhin, A. (2008) 'The approximability of MAX CSP with fixed-value constraints.', Journal of the ACM., 55 (4). p. 16.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Publisher 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},
Date accepted:No date available
Date deposited:30 July 2010
Date of first online publication:September 2008
Date first made open access:21 December 2022

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