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.SWAT.2016.5
URN: urn:nbn:de:0030-drops-60349
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6034/
Go to the corresponding LIPIcs Volume Portal

Mnich, Matthias ; Rutter, Ignaz ; Schmidt, Jens M.

Linear-Time Recognition of Map Graphs with Outerplanar Witness

pdf-format:
LIPIcs-SWAT-2016-5.pdf (0.5 MB)

Abstract

Map graphs generalize planar graphs and were introduced by Chen, Grigni and Papadimitriou [STOC 1998, J.ACM 2002]. They showed that the problem of recognizing map graphs is in NP by proving the existence of a planar witness graph W. Shortly after, Thorup [FOCS 1998] published a polynomial-time recognition algorithm for map graphs. However, the run time of this algorithm is estimated to be Omega(n^{120}) for n-vertex graphs, and a full description of its details remains unpublished.

We give a new and purely combinatorial algorithm that decides whether a graph G is a map graph having an outerplanar witness W. This is a step towards a first combinatorial recognition algorithm for general map graphs. The algorithm runs in time and space O(n+m). In contrast to Thorup's approach, it computes the witness graph W in the affirmative case.

BibTeX - Entry

@InProceedings{mnich_et_al:LIPIcs:2016:6034,
  author =	{Matthias Mnich and Ignaz Rutter and Jens M. Schmidt},
  title =	{{Linear-Time Recognition of Map Graphs with Outerplanar Witness}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Rasmus Pagh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6034},
  URN =		{urn:nbn:de:0030-drops-60349},
  doi =		{10.4230/LIPIcs.SWAT.2016.5},
  annote =	{Keywords: Algorithms and data structures, map graphs, recognition, planar graphs}
}

Keywords: Algorithms and data structures, map graphs, recognition, planar graphs
Collection: 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)
Issue Date: 2016
Date of publication: 22.06.2016

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI