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

  • Jakub Łącki
  • Piotr Sankowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)


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.


Short Path Planar Graph Short Cycle Original Graph Recursive Call 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jakub Łącki
    • 1
  • Piotr Sankowski
    • 1
  1. 1.Institute of InformaticsUniversity of WarsawWarsawPoland

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