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The girth of a graph is the length of its shortest cycle. We give analgorithm 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 isan improvement of a previous time bound of O(n^(3/2)), a bound which was onlyvalid for non-negative edge-weights. Our algorithm can be modified to output ashortest cycle within the same time and space bounds if such a cycle exists.

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