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Computing shortest cycles using universal covering space

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Abstract

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.

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Authors and Affiliations

  1. Computer Science Department, State University of New York at Stony Brook, Stony Brook, NY, 11790, USA

    Xiaotian Yin, Miao Jin & Xianfeng Gu

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  1. Xiaotian Yin
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  2. Miao Jin
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  3. Xianfeng Gu
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Correspondence to Xiaotian Yin.

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Yin, X., Jin, M. & Gu, X. Computing shortest cycles using universal covering space. Visual Comput 23, 999–1004 (2007). https://doi.org/10.1007/s00371-007-0169-9

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