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

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

2009-08-05

arxiv.org/abs/0908.0697v1

Computer Science

Discrete Mathematics

8 pages, no figures, zip file containing tex and pdf file

Scientific paper

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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