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arXiv · 0908.0697

Girth of a Planar Digraph with Real Edge Weights in O(n(log n)^3) Time

Christian Wulff-Nilsen
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Abstract

The girth of a graph is the length of its shortest cycle. We give an algorithm that computes in O(n(log n)^3) time and O(n) space the (weighted) girth of an n-vertex planar digraph with arbitrary real edge weights. This is an improvement of a previous time bound of O(n^(3/2)), a bound which was only valid for non-negative edge-weights. Our algorithm can be modified to output a shortest cycle within the same time and space bounds if such a cycle exists.

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Christian Wulff-Nilsen. 2009-08-05. Girth of a Planar Digraph with Real Edge Weights in O(n(log n)^3) Time. https://arxiv.org/abs/0908.0697

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