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

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Deineko, Vladimir G., Jonsson, P., Klasson, Mikael and Krokhin, Andrei.
(2008)
*The approximability of MAX CSP with fixed-value constraints.*
Association for Computing Machinery Journal, Vol.55
(No.4).
ISSN 0004-5411

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1145/1391289.1391290

## 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.

Item Type: | Journal Article |
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Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |

Divisions: | Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Social Sciences > Warwick Business School |

Library of Congress Subject Headings (LCSH): | Algorithms, Computational complexity, Approximation theory, Combinatorial optimization |

Journal or Publication Title: | Association for Computing Machinery Journal |

Publisher: | Association for Computing Machinery, Inc. |

ISSN: | 0004-5411 |

Official Date: | September 2008 |

Volume: | Vol.55 |

Number: | No.4 |

Number of Pages: | 37 |

Identification Number: | 10.1145/1391289.1391290 |

Status: | Peer Reviewed |

Publication Status: | Published |

Access rights to Published version: | Restricted or Subscription Access |

Funder: | University of Warwick. Centre for Discrete Mathematics and its Applications (DIMAP), Universitetet i Linköping. Center for Industrial Information Technology (CENIIT), Sweden. Vetenskapsrådet [Swedish Research Council], Engineering and Physical Sciences Research Council (EPSRC) |

Grant number: | 04.01 (CENIIT), 621-2003-3421 (SRC), 2006-4532 (SRC), EP/C543831/1 (EPSRC) |

References: | ALIMONTI, P., AND KANN, V. 2000. Some APX-completeness results for cubic graphs. Theoret. Comput. |

URI: | http://wrap.warwick.ac.uk/id/eprint/29330 |

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