research-article

The approximability of MAX CSP with fixed-value constraints

Authors:

Vladimir Deineko,

Mikael Klasson,

Andrei KrokhinAuthors Info & Claims

Journal of the ACM (JACM), Volume 55, Issue 4

Article No.: 16, Pages 1 - 37

https://doi.org/10.1145/1391289.1391290

Published: 18 September 2008 Publication History

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 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.

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Cited By

Jansen BWłodarczyk M(2023)Optimal Polynomial-Time Compression for Boolean Max CSPACM Transactions on Computation Theory10.1145/362470416:1(1-20)Online publication date: 26-Sep-2023
https://dl.acm.org/doi/10.1145/3624704
Kawarabayashi KXu C(2020)Minimum Violation Vertex Maps and Their Applications to Cut ProblemsSIAM Journal on Discrete Mathematics10.1137/19M129089934:4(2183-2207)Online publication date: 22-Oct-2020
https://doi.org/10.1137/19M1290899
Wareham T(2019)Designing Robot Teams for Distributed Construction, Repair, and MaintenanceACM Transactions on Autonomous and Adaptive Systems10.1145/333779714:1(1-29)Online publication date: 19-Jul-2019
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Index Terms

The approximability of MAX CSP with fixed-value constraints
1. Theory of computation
  1. Design and analysis of algorithms

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cover image Journal of the ACM

Journal of the ACM Volume 55, Issue 4

September 2008

170 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/1391289

Issue’s Table of Contents

Copyright © 2008 ACM.

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Publication History

Published: 18 September 2008

Accepted: 01 June 2008

Revised: 01 June 2008

Received: 01 November 2005

Published in JACM Volume 55, Issue 4

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Cited By

Jansen BWłodarczyk M(2023)Optimal Polynomial-Time Compression for Boolean Max CSPACM Transactions on Computation Theory10.1145/362470416:1(1-20)Online publication date: 26-Sep-2023
https://dl.acm.org/doi/10.1145/3624704
Kawarabayashi KXu C(2020)Minimum Violation Vertex Maps and Their Applications to Cut ProblemsSIAM Journal on Discrete Mathematics10.1137/19M129089934:4(2183-2207)Online publication date: 22-Oct-2020
https://doi.org/10.1137/19M1290899
Wareham T(2019)Designing Robot Teams for Distributed Construction, Repair, and MaintenanceACM Transactions on Autonomous and Adaptive Systems10.1145/333779714:1(1-29)Online publication date: 19-Jul-2019
https://dl.acm.org/doi/10.1145/3337797
Dalmau VKrokhin AManokaran R(2018)Towards a characterization of constant-factor approximable finite-valued CSPsJournal of Computer and System Sciences10.1016/j.jcss.2018.03.00397(14-27)Online publication date: Nov-2018
https://doi.org/10.1016/j.jcss.2018.03.003
Lin CShen WHawkins R(2017)Support for safety case generation via model transformationACM SIGBED Review10.1145/3076125.307613014:2(44-52)Online publication date: 31-Mar-2017
https://dl.acm.org/doi/10.1145/3076125.3076130
Jiang ZAbbas HMosterman PMangharam R(2017)Automated closed-loop model checking of implantable pacemakers using abstraction treesACM SIGBED Review10.1145/3076125.307612714:2(15-23)Online publication date: 31-Mar-2017
https://dl.acm.org/doi/10.1145/3076125.3076127
Kolmogorov VKrokhin ARolínek M(2017)The Complexity of General-Valued CSPsSIAM Journal on Computing10.1137/16M109183646:3(1087-1110)Online publication date: Jan-2017
https://doi.org/10.1137/16M1091836
Thapper JŽivný S(2016)The Complexity of Finite-Valued CSPsJournal of the ACM10.1145/297401963:4(1-33)Online publication date: 21-Sep-2016
https://dl.acm.org/doi/10.1145/2974019
Dalmau VKrokhin AManokaran RIndyk P(2015)Towards a characterization of constant-factor approximable Min CSPsProceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms10.5555/2722129.2722187(847-857)Online publication date: 4-Jan-2015
https://dl.acm.org/doi/10.5555/2722129.2722187
Kolmogorov VThapper JZźivnyź S(2015)The Power of Linear Programming for General-Valued CSPsSIAM Journal on Computing10.1137/13094564844:1(1-36)Online publication date: 5-Feb-2015
https://dl.acm.org/doi/10.1137/130945648
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