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Computing Shortest Cycles Using Universal Covering Space

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3 Author(s)
Xiaotian Yin ; Computer Science Department, State University of New York at Stony Brook, Stony Brook, NY, USA. xyin@cs.sunysb.edu ; Miao Jin ; Xianfeng Gu

Summary form only given. In this paper we generalize the shortest path algorithm to the shortest cycles in each homotopy class on a surface with arbitrary topology, utilizing the universal covering space (UCS) in algebraic topology. In order to store and handle the UCS, we propose a two-level data structure which is efficient for storage and easy to process. We also pointed several practical applications for our shortest cycle algorithms and the UCS data structure.

Published in:

Computer-Aided Design and Computer Graphics, 2007 10th IEEE International Conference on

Date of Conference:

15-18 Oct. 2007