# Constraint solving via fractional edge covers

Grohe, M and Marx, Dániel
(2014)
*Constraint solving via fractional edge covers.*
ACM TRANSACTIONS ON ALGORITHMS, 11 (1).
p. 4.
ISSN 1549-6325
10.1145/2636918

Text
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## Abstract

Many important combinatorial problems can be modeled as constraint satisfaction problems. Hence, identifying polynomial-time solvable classes of constraint satisfaction problems has received a lot of attention. In this article, we are interested in structural properties that can make the problem tractable. So far, the largest structural class that is known to be polynomial-time solvable is the class of bounded hypertree width instances introduced by Gottlob et al. [2002]. Here we identify a new class of polynomial-time solvable instances: those having bounded fractional edge cover number. Combining hypertree width and fractional edge cover number, we then introduce the notion of fractional hypertree width. We prove that constraint satisfaction problems with bounded fractional hypertree width can be solved in polynomial time (provided that the tree decomposition is given in the input). Together with a recent approximation algorithm for finding such decompositions [Marx 2010], it follows that bounded fractional hypertree width is now the most generally known structural property that guarantees polynomial-time solvability.

Item Type: | Article |
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Uncontrolled Keywords: | Hyper graph; Edge cover; Constraint solving; Hypertree width; hypergraphs; Fractional edge covers; Constraint satisfaction |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Divisions: | Informatics Laboratory |

SWORD Depositor: | MTMT Injector |

Depositing User: | MTMT Injector |

Date Deposited: | 26 Sep 2014 19:15 |

Last Modified: | 26 Sep 2014 19:15 |

URI: | https://eprints.sztaki.hu/id/eprint/8000 |

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