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### Tractable Structures for Constraint Satisfaction with Truth Tables

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### Abstract

The way the graph structure of the constraints influences the complexity of constraint satisfaction problems (CSP) is well understood for bounded-arity constraints. The situation is less clear if there is no bound on the arities. In this case the answer depends also on how the constraints are represented in the input. We study this question for the truth table representation of constraints. We introduce a new hypergraph measure {\em adaptive width} and show that CSP with truth tables is polynomial-time solvable if restricted to a class of hypergraphs with bounded adaptive width. Conversely, assuming a conjecture on the complexity of binary CSP, there is no other polynomial-time solvable case.

### BibTeX - Entry

@InProceedings{marx:LIPIcs:2009:1807,
author =	{Daniel Marx},
title =	{{Tractable Structures for Constraint Satisfaction with Truth Tables}},
booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
pages =	{649--660},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-09-5},
ISSN =	{1868-8969},
year =	{2009},
volume =	{3},
editor =	{Susanne Albers and Jean-Yves Marion},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/1807},
URN =		{urn:nbn:de:0030-drops-18079},
doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2009.1807},
annote =	{Keywords: Computational complexity, Constraint satisfaction, Treewidth, Adaptive width}
}


 Keywords: Computational complexity, Constraint satisfaction, Treewidth, Adaptive width Seminar: 26th International Symposium on Theoretical Aspects of Computer Science Issue date: 2009 Date of publication: 2009

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