Girth of a Planar Digraph with Real Edge Weights in O(n(log n)^3) Time
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2009
- DOI:
- 10.48550/arXiv.0908.0697
- arXiv:
- arXiv:0908.0697
- Bibcode:
- 2009arXiv0908.0697W
- Keywords:
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- Computer Science - Discrete Mathematics;
- G.2.2
- E-Print:
- 8 pages, no figures, zip file containing tex and pdf file