Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
Proceedings of the twenty-second annual symposium on Computational geometry（2006）
摘要
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.
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关键词
shortest non-contractible,central open problem,system of loops,n log n,current-best o,orientable combinatorial surface,efficient algorithm,computational topology,orientable surface,planar graph,computing shortest non-trivial cycle,n denotes,ecien t algorithm,universal cover,non-trivial cycles,time algorithm,linear time,bounded genus,shortest non-separating cycle
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