Min-cuts and shortest cycles in planar graphs in O(n log log n) time

Authors:
Jakub Łącki;Piotr Sankowski
Affiliations:
Institute of Informatics, University of Warsaw, Warsaw, Poland;Institute of Informatics, University of Warsaw, Warsaw, Poland
Venue:
ESA'11 Proceedings of the 19th European conference on Algorithms
Year:
2011

Citing 11
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Abstract

We present a deterministic O(n log log n) 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 log n. 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(n5/6 log5/2 n) time dynamic algorithm al well.