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Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time

Martin Kutz
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Abstract

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(n^{3/2})-time algorithm by Cabello and Mohar (ESA 2005). Our algorithm uses universal-cover constructions to find short cycles and makes extensive use of existing tools from the field.

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Martin Kutz. 2005-12-15. Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time. https://arxiv.org/abs/cs/0512064

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