Computing Shortest Non-Trivial Cycles on Orientable Surfaces of Bounded Genus 
in Almost Linear Time.

Kutz, Martin; Amenta, Nina; Cheong, Otfried

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Computing Shortest Non-Trivial Cycles on Orientable Surfaces of Bounded Genus in Almost Linear Time.

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Kutz, Martin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Kutz, M. (2006). Computing Shortest Non-Trivial Cycles on Orientable Surfaces of Bounded Genus in Almost Linear Time. In Proceedings of the 22nd Annual Symposium on Computational Geometry, SCG'06 (pp. 430-437). New York, USA: ACM.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-2261-F

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 $O(n \frac{3}{2})$-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.