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DOI: 10.4230/LIPIcs.FSTTCS.2008.1749
URN: urn:nbn:de:0030-drops-17491
URL: http://drops.dagstuhl.de/opus/volltexte/2008/1749/
Datta, Samir ; Limaye, Nutan ; Nimbhorkar, Prajakta

3-connected Planar Graph Isomorphism is in Log-space

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Abstract

We consider the isomorphism and canonization problem for $3$-connected planar graphs. The problem was known to be \Log-hard and in \ULcoUL\ \cite{TW07}. In this paper, we give a deterministic log-space algorithm for $3$-connected planar graph isomorphism and canonization. This gives an \Log-completeness result, thereby settling its complexity. \par The algorithm uses the notion of universal exploration sequences from \cite{koucky01} and \cite{Rei05}. To our knowledge, this is a completely new approach to graph canonization.

BibTeX - Entry

@InProceedings{datta_et_al:LIPIcs:2008:1749,
  author =	{Samir Datta and Nutan Limaye and Prajakta Nimbhorkar},
  title =	{3-connected Planar Graph Isomorphism is in Log-space},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008)},
  pages =	{155--162},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Ramesh Hariharan and Madhavan Mukund and V Vinay},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1749},
  URN =		{urn:nbn:de:0030-drops-17491},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2008.1749},
  annote =	{Keywords: Planar graph isomorphism, three connected graphs, logspace, universal exploration sequence}
}

Keywords: Planar graph isomorphism, three connected graphs, logspace, universal exploration sequence
Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Issue date: 2008
Date of publication: 05.12.2008

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