Minimum S - T cut in undirected planar graphs when the source and the sink are close

Haim Kaplan, Yahav Nussbaum

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publication28th International Symposium on Theoretical Aspects of Computer Science, STACS 2011
Pages117-128
Number of pages12
DOIs
StatePublished - 2011
Event28th International Symposium on Theoretical Aspects of Computer Science, STACS 2011 - Dortmund, Germany
Duration: 10 Mar 201112 Mar 2011

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume9
ISSN (Print)1868-8969

Conference

Conference28th International Symposium on Theoretical Aspects of Computer Science, STACS 2011
Country/TerritoryGermany
CityDortmund
Period10/03/1112/03/11

Keywords

  • Cut cycle
  • Minimum cut
  • Planar graph
  • Shortest path

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