Finding k Disjoint Paths in a Directed Planar Graph

Abstract

Previous article Next article Finding k Disjoint Paths in a Directed Planar GraphAlexander SchrijverAlexander Schrijverhttps://doi.org/10.1137/S0097539792224061PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIt is shown that, for each fixed k, the problem of finding k pairwise vertex-disjoint directed paths between given pairs of terminals in a directed planar graph is solvable in polynomial time.[1] Steven Fortune, , John Hopcroft and , James Wyllie, The directed subgraph homeomorphism problem, Theoret. Comput. Sci., 10 (1980), 111–121 10.1016/0304-3975(80)90009-2 81e:68079 0419.05028 CrossrefISIGoogle Scholar[2] J. F. Lynch, The equivalence of theorem proving and the interconnection problem, (ACM) SIGDA Newsletter, 5, 3 (1975), 31–36 CrossrefGoogle Scholar[3] B. A. Reed, , N. Robertson, , A. Schrijver and , P. D. Seymour, N. Robertson and , P. D. 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Geom., 6 (1991), 527–574 92f:05039 0755.05033 CrossrefISIGoogle ScholarKeywordsdisjointpathdirectedplanargraphpolynomial-timealgorithmfree grouphomologouscoho-mologous Previous article Next article FiguresRelatedReferencesCited byDetails Polynomial Time Algorithms for Tracking Path Problems8 February 2022 | Algorithmica, Vol. 84, No. 6 Cross Ref Combinatorial acyclicity models for potential‐based flows9 April 2021 | Networks, Vol. 79, No. 1 Cross Ref Theoretical Groundwork21 October 2021 Cross Ref A relaxation of the Directed Disjoint Paths problem: A global congestion metric helpsTheoretical Computer Science, Vol. 898 Cross Ref Strong Subgraph Connectivity of Digraphs: A Survey12 June 2021 | Journal of Interconnection Networks, Vol. 21, No. 04 Cross Ref On finding maximum disjoint paths with different colors: Computational complexity and practical LP-based algorithmsTheoretical Computer Science, Vol. 886 Cross Ref A Tight Lower Bound for Edge-Disjoint Paths on Planar DAGs4 May 2021 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An Annotated Tableau Cross Ref Volume 23, Issue 4| 1994SIAM Journal on Computing History Submitted:02 January 1992Accepted:26 April 1993Published online:13 July 2006 InformationCopyright © 1994 Society for Industrial and Applied MathematicsKeywordsdisjointpathdirectedplanargraphpolynomial-timealgorithmfree grouphomologouscoho-mologousMSC codes05C2005C8568R10PDF Download Article & Publication DataArticle DOI:10.1137/S0097539792224061Article page range:pp. 780-788ISSN (print):0097-5397ISSN (online):1095-7111Publisher:Society for Industrial and Applied Mathematics