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Flows in One-Crossing-Minor-Free Graphs

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Algorithms and Computation (ISAAC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6506))

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Abstract

We study the maximum flow problem in directed H-minor-free graphs where H can be drawn in the plane with one crossing. If a structural decomposition of the graph as a clique-sum of planar graphs and graphs of constant complexity is given, we show that a maximum flow can be computed in O(nlogn) time. In particular, maximum flows in directed K 3,3-minor-free graphs and directed K 5-minor-free graphs can be computed in O(nlogn) time without additional assumptions.

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Author information

Authors and Affiliations

  1. Dept. of Mathematics and Computer Science, Saint Louis University, USA

    Erin Chambers

  2. Computer Science Department, University of California, Irvine, USA

    David Eppstein

Authors
  1. Erin Chambers
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  2. David Eppstein
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Editors and Affiliations

  1. Department of Computer Science, KAIST, Gwahangno 335, 305-701, Yuseong-gu, Daejeon, Korea

    Otfried Cheong  & Kyung-Yong Chwa  & 

  2. School of Computer Science and Engineering, Seoul National University, 151-742, Seoul, Korea

    Kunsoo Park

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Chambers, E., Eppstein, D. (2010). Flows in One-Crossing-Minor-Free Graphs. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17517-6_23

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  • DOI: https://doi.org/10.1007/978-3-642-17517-6_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17516-9

  • Online ISBN: 978-3-642-17517-6

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