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DOI: 10.4230/OASIcs.SOSA.2019.14
URN: urn:nbn:de:0030-drops-100409
URL: http://drops.dagstuhl.de/opus/volltexte/2018/10040/
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Kotrbcík, Michal ; Skoviera, Martin

Simple Greedy 2-Approximation Algorithm for the Maximum Genus of a Graph

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Abstract

The maximum genus gamma_M(G) of a graph G is the largest genus of an orientable surface into which G has a cellular embedding. Combinatorially, it coincides with the maximum number of disjoint pairs of adjacent edges of G whose removal results in a connected spanning subgraph of G. In this paper we describe a greedy 2-approximation algorithm for maximum genus by proving that removing pairs of adjacent edges from G arbitrarily while retaining connectedness leads to at least gamma_M(G)/2 pairs of edges removed. As a consequence of our approach we also obtain a 2-approximate counterpart of Xuong's combinatorial characterisation of maximum genus.

BibTeX - Entry

@InProceedings{kotrbck_et_al:OASIcs:2018:10040,
  author =	{Michal Kotrbc{\'i}k and Martin Skoviera},
  title =	{{Simple Greedy 2-Approximation Algorithm for the Maximum Genus of a Graph}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{14:1--14:9},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{69},
  editor =	{Jeremy T. Fineman and Michael Mitzenmacher},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10040},
  URN =		{urn:nbn:de:0030-drops-100409},
  doi =		{10.4230/OASIcs.SOSA.2019.14},
  annote =	{Keywords: maximum genus, embedding, graph, greedy algorithm}
}

Keywords: maximum genus, embedding, graph, greedy algorithm
Seminar: 2nd Symposium on Simplicity in Algorithms (SOSA 2019)
Issue Date: 2018
Date of publication: 18.12.2018


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