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.2017.19
URN: urn:nbn:de:0030-drops-85597
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8559/
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Hlineny, Petr ; Pokrývka, Filip ; Roy, Bodhayan

FO Model Checking of Geometric Graphs

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LIPIcs-IPEC-2017-19.pdf (0.5 MB)

Abstract

Over the past two decades the main focus of research into first-order (FO) model checking algorithms has been on sparse relational structures – culminating in the FPT algorithm by Grohe, Kreutzer and Siebertz for FO model checking of nowhere dense classes of graphs. On contrary to that, except the case of locally bounded clique-width only little is currently known about FO model checking of dense classes of graphs or other structures. We study the FO model checking problem for dense graph classes definable by geometric means (intersection and visibility graphs). We obtain new nontrivial FPT results, e.g., for restricted subclasses of circular-arc, circle, box, disk, and polygon-visibility graphs. These results use the FPT algorithm by Gajarský et al. for FO model checking of posets of bounded width. We also complement the tractability results by related hardness reductions.

BibTeX - Entry

@InProceedings{hlineny_et_al:LIPIcs:2018:8559,
  author =	{Petr Hlineny and Filip Pokr{\'y}vka and Bodhayan Roy},
  title =	{{FO Model Checking of Geometric Graphs}},
  booktitle =	{12th International Symposium on Parameterized and Exact Computation (IPEC 2017)},
  pages =	{19:1--19:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-051-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{89},
  editor =	{Daniel Lokshtanov and Naomi Nishimura},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8559},
  URN =		{urn:nbn:de:0030-drops-85597},
  doi =		{10.4230/LIPIcs.IPEC.2017.19},
  annote =	{Keywords: first-order logic, model checking, fixed-parameter tractability, intersection graphs, visibility graphs}
}

Keywords: first-order logic, model checking, fixed-parameter tractability, intersection graphs, visibility graphs
Collection: 12th International Symposium on Parameterized and Exact Computation (IPEC 2017)
Issue Date: 2018
Date of publication: 02.03.2018

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