License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.IPEC.2016.14
URN: urn:nbn:de:0030-drops-69412
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/6941/
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Gaspers, Serge ; Papadimitriou, Christos H. ; Sæther, Sigve Hortemo ; Telle, Jan Arne

On Satisfiability Problems with a Linear Structure

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LIPIcs-IPEC-2016-14.pdf (0.6 MB)

Abstract

It was recently shown [Sæther, Telle, and Vatshelle, JAIR 54, 2015] that satisfiability is polynomially solvable when the incidence graph is an interval bipartite graph (an interval graph turned into a bipartite graph by omitting all edges within each partite set). Here we relax this condition in several directions: First, we show an FPT algorithm parameterized by k for k-interval bigraphs, bipartite graphs which can be converted to interval bipartite graphs by adding to each node of one side at most k edges; the same result holds for the counting and the weighted maximization version of satisfiability. Second, given two linear orders, one for the variables and one for the clauses, we show how to find, in polynomial time, the smallest k such that there is a k-interval bigraph compatible with these two orders. On the negative side we prove that, barring complexity collapses, no such extensions are possible for CSPs more general than satisfiability. We also show NP-hardness of recognizing 1-interval
bigraphs.

BibTeX - Entry

@InProceedings{gaspers_et_al:LIPIcs:2017:6941,
  author =	{Serge Gaspers and Christos H. Papadimitriou and Sigve Hortemo Sæther and Jan Arne Telle},
  title =	{{On Satisfiability Problems with a Linear Structure}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Jiong Guo and Danny Hermelin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/6941},
  URN =		{urn:nbn:de:0030-drops-69412},
  doi =		{10.4230/LIPIcs.IPEC.2016.14},
  annote =	{Keywords: Satisfiability, interval graphs, FPT algorithms}
}

Keywords: Satisfiability, interval graphs, FPT algorithms
Collection: 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)
Issue Date: 2017
Date of publication: 09.02.2017

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