Abstract
An essential cycle on a surface is a simple cycle that cannot be continuously deformed to a point or a single boundary. We describe algorithms to compute the shortest essential cycle in an orientable combinatorial surface in O(n 2log n) time, or in O(nlog n) time when both the genus and number of boundaries are fixed. Our results correct an error in a paper of Erickson and Har-Peled (Discrete Comput. Geom. 31(1):37–59, 2004).
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Research reported in this paper was partially supported by NSF grant DMS-0528086. See http://www.cs.uiuc.edu/~jeffe/pubs/essential.html for the most recent version of this paper.
This work was done while the second author was affiliated with the University of Illinois, Urbana-Champaign.
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Erickson, J., Worah, P. Computing the Shortest Essential Cycle. Discrete Comput Geom 44, 912–930 (2010). https://doi.org/10.1007/s00454-010-9241-8
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DOI: https://doi.org/10.1007/s00454-010-9241-8