NDLI: The approximability of MAX CSP with fixed-value constraints

Content Provider	ACM Digital Library
Author	Deineko, Vladimir Jonsson, Peter Klasson, Mikael Krokhin, Andrei
Copyright Year	2008
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 $\textit{x}$ = $\textit{a}),$ 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.
Starting Page	1
Ending Page	37
Page Count	37
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/1391289.1391290
Journal	Journal of the ACM (JACM)
Volume Number	55
Issue Number	4
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2008-09-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Complexity of approximation Monge properties Dichotomy Maximum constraint satisfaction Supermodularity
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

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