Fast algorithms for shortest paths in planar graphs, with applications
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Faster shortest-path algorithms for planar graphs
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We present an algorithm that computes a shortest non-contractible and a shortest non-separating cycle on an orientable combinatorial surface of bounded genus in O(n log n) time, where n denotes the complexity of the surface. This solves a central open problem in computational topology, improving upon the current-best O(n3/2)-time algorithm by Cabello and Mohar (ESA 2005). Our algorithm is based on universal-cover constructions to find short cycles and makes extensive use of existing tools from the field.