A Polynomial-Time Algorithm for Planar Multicuts with Few Source-Sink Pairs

  • Cédric Bentz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7535)


Given an edge-weighted undirected graph and a list of k source-sink pairs of vertices, the well-known minimum multicut problem consists in selecting a minimum-weight set of edges whose removal leaves no path between every source and its corresponding sink. We give the first polynomial-time algorithm to solve this problem in planar graphs, when k is fixed. Previously, this problem was known to remain NP-hard in general graphs with fixed k, and in trees with arbitrary k; the most noticeable tractable case known so far was in planar graphs with fixed k and sources and sinks lying on the outer face.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Cédric Bentz
    • 1
  1. 1.LRI, Univ. Paris-Sud & CNRSOrsay CedexFrance

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