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Min-Cuts and Shortest Cycles in Planar Graphs in O(n loglogn) Time

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Algorithms – ESA 2011 (ESA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6942))

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Abstract

We present a deterministic O(n loglogn) time algorithm for finding shortest cycles and minimum cuts in planar graphs. The algorithm improves the previously known fastest algorithm by Italiano et al. in STOC’11 by a factor of logn. This speedup is obtained through the use of dense distance graphs combined with a divide-and-conquer approach. Extending this approach we are able to show an O(n 5/6 log5/2 n) time dynamic algorithm al well.

This work has been partially supported by the Polish Ministry of Science, Grant N N206 355636 and by the ERC StG Project PAAl no. 259515.

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Jakub Łącki & Piotr Sankowski

Authors
  1. Jakub Łącki
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  2. Piotr Sankowski
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Editors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, University of Rome " La Sapienza", via Ariosto 25, 00185, Roma, Italy

    Camil Demetrescu

  2. School of Computer Science, Reykjavik University, Menntavegur 1, 101, Reykjavik, Iceland

    Magnús M. Halldórsson

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Łącki, J., Sankowski, P. (2011). Min-Cuts and Shortest Cycles in Planar Graphs in O(n loglogn) Time. In: Demetrescu, C., Halldórsson, M.M. (eds) Algorithms – ESA 2011. ESA 2011. Lecture Notes in Computer Science, vol 6942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23719-5_14

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  • DOI: https://doi.org/10.1007/978-3-642-23719-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23718-8

  • Online ISBN: 978-3-642-23719-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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