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.2008.1347
URN: urn:nbn:de:0030-drops-13474
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1347/
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Colin de Verdiére, Éric ; Schrijver, Alexander

Shortest Vertex-Disjoint Two-Face Paths in Planar Graphs

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Abstract

Let $G$ be a directed planar graph of complexity~$n$, each arc
having a nonnegative length. Let $s$ and~$t$ be two distinct faces
of~$G$; let $s_1,ldots,s_k$ be vertices incident with~$s$; let
$t_1,ldots,t_k$ be vertices incident with~$t$. We give an
algorithm to compute $k$ pairwise vertex-disjoint paths connecting
the pairs $(s_i,t_i)$ in~$G$, with minimal total length, in
$O(knlog n)$ time.

BibTeX - Entry

@InProceedings{colindeverdire_et_al:LIPIcs:2008:1347,
  author =	{{\'E}ric Colin de Verdi{\'e}re and Alexander Schrijver},
  title =	{{Shortest Vertex-Disjoint Two-Face Paths in Planar Graphs}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{181--192},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Susanne Albers and Pascal Weil},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1347},
  URN =		{urn:nbn:de:0030-drops-13474},
  doi =		{10.4230/LIPIcs.STACS.2008.1347},
  annote =	{Keywords: Algorithm, planar graph, disjoint paths, shortest path}
}

Keywords: Algorithm, planar graph, disjoint paths, shortest path
Collection: 25th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2008
Date of publication: 06.02.2008

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