License: Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2009.1835
URN: urn:nbn:de:0030-drops-18355
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/1835/
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Borradaile, Glencora ; Demaine, Erik D. ; Tazari, Siamak

Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs

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Abstract

We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The schemes run in $O(n \log n)$ time for graphs embedded on both orientable and non-orientable surfaces. This work generalizes the PTAS frameworks of Borradaile, Klein, and Mathieu (2007 and 2006) from planar graphs to bounded-genus graphs: any future problems shown to admit the required structure theorem for planar graphs will similarly extend to bounded-genus graphs.

BibTeX - Entry

@InProceedings{borradaile_et_al:LIPIcs:2009:1835,
  author =	{Glencora Borradaile and Erik D. Demaine and Siamak Tazari},
  title =	{{Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{171--182},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Susanne Albers and Jean-Yves Marion},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/1835},
  URN =		{urn:nbn:de:0030-drops-18355},
  doi =		{10.4230/LIPIcs.STACS.2009.1835},
  annote =	{Keywords: Polynomial-time approximation scheme, Bounded-genus graph, Embedded graph, Steiner tree, Survivable-network design, Subset TSP}
}

Keywords: Polynomial-time approximation scheme, Bounded-genus graph, Embedded graph, Steiner tree, Survivable-network design, Subset TSP
Collection: 26th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2009
Date of publication: 19.02.2009

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