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DOI: 10.4230/LIPIcs.STACS.2011.117

Minimum s-t cut in undirected planar graphs when the source and the sink are close

Authors: Haim Kaplan and Yahav Nussbaum

Published in: LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

Abstract

Consider the minimum s-t cut problem in an embedded undirected planar graph. Let p be the minimum number of faces that a curve from s to $t$ passes through. If p=1, that is, the vertices s and t are on the boundary of the same face, then the minimum cut can be found in O(n)time. For general planar graphs this cut can be found in O(n log n) time. We unify these results and give an O(n log p) time algorithm. We use cut-cycles to obtain the value of the minimum cut, and study the structure of these cycles to get an efficient algorithm.

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Haim Kaplan and Yahav Nussbaum. Minimum s-t cut in undirected planar graphs when the source and the sink are close. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 117-128, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{kaplan_et_al:LIPIcs.STACS.2011.117,
  author =	{Kaplan, Haim and Nussbaum, Yahav},
  title =	{{Minimum s-t cut in undirected planar graphs when the source and the sink are close}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{117--128},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.117},
  URN =		{urn:nbn:de:0030-drops-30049},
  doi =		{10.4230/LIPIcs.STACS.2011.117},
  annote =	{Keywords: planar graph, minimum cut, shortest path, cut cycle}
}

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Minimum s-t cut in undirected planar graphs when the source and the sink are close

Abstract

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