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.2017.5
URN: urn:nbn:de:0030-drops-85487
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8548/
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Baste, Julien ; Thilikos, Dimitrios M.

Contraction-Bidimensionality of Geometric Intersection Graphs

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LIPIcs-IPEC-2017-5.pdf (1 MB)

Abstract

Given a graph G, we define bcg(G) as the minimum k for which G can be contracted to the uniformly triangulated grid Gamma_k. A graph class G has the SQGC property if every graph G in G has treewidth O(bcg(G)c) for some 1 <= c < 2. The SQGC property is important for algorithm design as it defines the applicability horizon of a series of meta-algorithmic results, in the framework of bidimensionality theory, related to fast parameterized algorithms, kernelization, and approximation schemes. These results apply to a wide family of problems, namely problems that are contraction-bidimensional. Our main combinatorial result reveals a general family of graph classes that satisfy the SQGC property and includes bounded-degree string graphs. This considerably extends the applicability of bidimensionality theory for several intersection graph classes of 2-dimensional geometrical objects.

BibTeX - Entry

@InProceedings{baste_et_al:LIPIcs:2018:8548,
  author =	{Julien Baste and Dimitrios M. Thilikos},
  title =	{{Contraction-Bidimensionality of Geometric Intersection Graphs}},
  booktitle =	{12th International Symposium on Parameterized and Exact Computation (IPEC 2017)},
  pages =	{5:1--5:13},
  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/2018/8548},
  URN =		{urn:nbn:de:0030-drops-85487},
  doi =		{10.4230/LIPIcs.IPEC.2017.5},
  annote =	{Keywords: Grid exlusion theorem, Bidimensionality, Geometric intersection graphs, String Graphs}
}

Keywords: Grid exlusion theorem, Bidimensionality, Geometric intersection graphs, String 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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