### The approximability of MAX CSP with fixed-value constraintsThe approximability of MAX CSP with fixed-value constraints

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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