Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
Computational Geometry
2007-05-23 v1
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.
Cite
@article{arxiv.cs/0512064,
title = {Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time},
author = {Martin Kutz},
journal= {arXiv preprint arXiv:cs/0512064},
year = {2007}
}
Comments
13 pages, 7 figures