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DOI: 10.4230/LIPIcs.STACS.2009.1835

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

Authors: Glencora Borradaile, Erik D. Demaine, and Siamak Tazari

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

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.

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Glencora Borradaile, Erik D. Demaine, and Siamak Tazari. Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 171-182, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{borradaile_et_al:LIPIcs.STACS.2009.1835,
  author =	{Borradaile, Glencora and Demaine, Erik D. and Tazari, Siamak},
  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 =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.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}
}

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

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