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arXiv · 1512.02068

Minimum Cut of Directed Planar Graphs in O(nloglogn) Time

Shay Mozes·Cyril Nikolaev·Yahav Nussbaum·Oren Weimann
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Abstract

We give an $O(n \log \log n)$ time algorithm for computing the minimum cut (or equivalently, the shortest cycle) of a weighted directed planar graph. This improves the previous fastest $O(n\log^3 n)$ solution. Interestingly, while in undirected planar graphs both min-cut and min $st$-cut have $O(n \log \log n)$ solutions, in directed planar graphs our result makes min-cut faster than min $st$-cut, which currently requires $O(n \log n)$.

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Shay Mozes, Cyril Nikolaev, Yahav Nussbaum, Oren Weimann. 2015-12-07. Minimum Cut of Directed Planar Graphs in O(nloglogn) Time. https://arxiv.org/abs/1512.02068

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