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/
Baste, Julien ;
Thilikos, Dimitrios M.
Contraction-Bidimensionality of Geometric Intersection Graphs
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: |
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Grid exlusion theorem, Bidimensionality, Geometric intersection graphs, String Graphs |
Collection: |
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12th International Symposium on Parameterized and Exact Computation (IPEC 2017) |
Issue Date: |
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2018 |
Date of publication: |
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02.03.2018 |