Computing maximum flows in undirected planar networks with both edge and vertex capacities

Xianchao Zhang*, Weifa Liang, Guoliang Chen

*Corresponding author for this work

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

    5 Citations (Scopus)

    Abstract

    We study the maximum flow problem in an undirected planar network with both edge and vertex capacities (EVC-network). A previous study reduces the minimum cut problem in an undirected planar EVC-network to the minimum edge-cut problem in another planar network with edge capacity only (EC-network), thus the minimum-cut or the maximum flow value can be computed in O(nlogn) time. Based on this reduction, in this paper we devise an O(nlogn) time algorithm for computing the maximum flow in an undirected general planar EVC-network and an O(n) time algorithm for computing the maximum flow in an undirected (s,t)-planar EVC-network. As a result, the maximum flow problem in undirected planar EVC-networks is as easy as the problem in undirected planar EC-networks in terms of computational complexity.

    Original languageEnglish
    Title of host publicationComputing and Combinatorics - 14th Annual International Conference, COCOON 2008, Proceedings
    Pages577-586
    Number of pages10
    DOIs
    Publication statusPublished - 2008
    Event14th Annual International Conference on Computing and Combinatorics, COCOON 2008 - Dalian, China
    Duration: 27 Jun 200829 Jun 2008

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume5092 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Conference

    Conference14th Annual International Conference on Computing and Combinatorics, COCOON 2008
    Country/TerritoryChina
    CityDalian
    Period27/06/0829/06/08

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