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.
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