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Sparsest Cut in Planar Graphs, Maximum Concurrent Flows and Their Connections with the Max-Cut Problem

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Integer Programming and Combinatorial Optimization (IPCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9682))

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Abstract

We study the sparsest cut problem when the “capacity-demand” graph is planar, and give a combinatorial algorithm. In this type of graphs there is an edge for each positive capacity and also an edge for each positive demand. We extend this result to graphs with no \(K_5\) minor. We also show how to find a maximum concurrent flow in these two cases. We use ideas that had been developed for the max-cut problem, and show how to exploit the connections among these problems.

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Author information

Authors and Affiliations

  1. CNRS, Université Clermont II, Campus des Cézeaux BP 125, 63173, Aubière Cedex, France

    Mourad Baïou

  2. IBM T. J. Watson Research Center, Yorktown Heights, NY, 10589, USA

    Francisco Barahona

Authors
  1. Mourad Baïou
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  2. Francisco Barahona
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Correspondence to Mourad Baïou .

Editor information

Editors and Affiliations

  1. Université de Liège, Liège, Belgium

    Quentin Louveaux

  2. Technische Universität Berlin, Berlin, Germany

    Martin Skutella

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Baïou, M., Barahona, F. (2016). Sparsest Cut in Planar Graphs, Maximum Concurrent Flows and Their Connections with the Max-Cut Problem. In: Louveaux, Q., Skutella, M. (eds) Integer Programming and Combinatorial Optimization. IPCO 2016. Lecture Notes in Computer Science(), vol 9682. Springer, Cham. https://doi.org/10.1007/978-3-319-33461-5_6

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  • DOI: https://doi.org/10.1007/978-3-319-33461-5_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33460-8

  • Online ISBN: 978-3-319-33461-5

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