Girth of a Planar Digraph with Real Edge Weights in O(n(log n)^3) Time
Discrete Mathematics
2009-08-06 v1
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.
Cite
@article{arxiv.0908.0697,
title = {Girth of a Planar Digraph with Real Edge Weights in O(n(log n)^3) Time},
author = {Christian Wulff-Nilsen},
journal= {arXiv preprint arXiv:0908.0697},
year = {2009}
}
Comments
8 pages, no figures, zip file containing tex and pdf file