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

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.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2261-F Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2262-D
Genre: Conference Paper

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 Creators:
Kutz, Martin1, Author           
Amenta, Nina, Editor
Cheong, Otfried, Editor
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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

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Language(s): eng - English
 Dates: 2007-04-162006
 Publication Status: Issued
 Pages: -
 Publishing info: New York, USA : ACM
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 314624
Other: Local-ID: C1256428004B93B8-D331462109CCC5B5C125729000424481-Kutz2006
 Degree: -

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Title: Untitled Event
Place of Event: Sedona, Arizona, USA
Start-/End Date: 2006-06-05

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Title: Proceedings of the 22nd Annual Symposium on Computational Geometry, SCG'06
Source Genre: Proceedings
 Creator(s):
Affiliations:
Publ. Info: New York, USA : ACM
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 430 - 437 Identifier: ISBN: 1-59593-340-9