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Counting Minimum (s,t)-Cuts in Weighted Planar Graphs in Polynomial Time

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Mathematical Foundations of Computer Science 2010 (MFCS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6281))

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Abstract

We give an O(nd + nlogn) algorithm computing the number of minimum (s,t)-cuts in weighted planar graphs, where n is the number of vertices and d is the length of the shortest s-t path in the corresponding unweighted graph. Previously, Ball and Provan gave a polynomial-time algorithm for unweighted graphs with both s and t lying on the outer face. Our results hold for all locations of s and t and weighted graphs, and have direct applications in image segmentation and other computer vision problems.

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Author information

Authors and Affiliations

  1. Rochester Institute of Technology, Rochester, NY, USA

    Ivona Bezáková

  2. IBM, Poughkeepsie, NY, USA

    Adam J. Friedlander

Authors
  1. Ivona Bezáková
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  2. Adam J. Friedlander
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Editor information

Editors and Affiliations

  1. Falculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Petr Hliněný

  2. Faculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Antonín Kučera

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Bezáková, I., Friedlander, A.J. (2010). Counting Minimum (s,t)-Cuts in Weighted Planar Graphs in Polynomial Time. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_13

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  • DOI: https://doi.org/10.1007/978-3-642-15155-2_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15154-5

  • Online ISBN: 978-3-642-15155-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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