Computing the shortest essential cycle

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(n2log n) time, or in O(n log 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). © 2010 Springer Science+Business Media, LLC.