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Author Deineko, Vladimir ♦ Jonsson, Peter ♦ Klasson, Mikael ♦ Krokhin, Andrei
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2008
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Complexity of approximation ♦ Monge properties ♦ Dichotomy ♦ Maximum constraint satisfaction ♦ Supermodularity
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.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2008-09-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 55
Issue Number 4
Page Count 37
Starting Page 1
Ending Page 37

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Source: ACM Digital Library