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.
| Original language | English |
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| Pages | 1-8 |
| Number of pages | 8 |
| Publication status | Published - 2009 |