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The approximability of MAX CSP with fixed-value constraints

โœ Scribed by Deineko, Vladimir; Jonsson, Peter; Klasson, Mikael; Krokhin, Andrei


Book ID
121432016
Publisher
Association for Computing Machinery
Year
2008
Tongue
English
Weight
321 KB
Volume
55
Category
Article
ISSN
0004-5411

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โœฆ Synopsis


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.


๐Ÿ“œ SIMILAR VOLUMES


The Approximability of Three-valued MAX
โœ Jonsson, Peter; Klasson, Mikael; Krokhin, Andrei ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Society for Industrial and Applied Mathematics ๐ŸŒ English โš– 240 KB