Geometric Approach to Optimal Path Problem with Uncertain Arc Lengths

  • Authors

    • Atefeh Hasan-Zadeh University of Tehran
    2020-07-25
    https://doi.org/10.14419/jacst.v9i1.30674
  • Shortest path problem, Homotopy, Covering space, Cycle

  • Abstract

    In this paper, the problem of finding the shortest paths, one of the most important problems in science and technology has been geometrically studied. Shortest path algorithm has been generalized to the shortest cycles in each homotopy class on a surface with arbitrary topology, using the universal covering space notion in the algebraic topology. Then, a general algorithm has been presented to compute the shortest cycles (geometrically rather than combinatorial) in each homotopy class. The algorithm can handle surface meshes with the desired topology, with or without boundary. It also provides a fundamental framework for other algorithms based on universal coverage space due to the capacity and flexibility of the framework.

     

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  • How to Cite

    Hasan-Zadeh, A. (2020). Geometric Approach to Optimal Path Problem with Uncertain Arc Lengths. Journal of Advanced Computer Science & Technology (JACST), 9(1), 11-13. https://doi.org/10.14419/jacst.v9i1.30674

    Received date: 2020-04-28

    Accepted date: 2020-07-17

    Published date: 2020-07-25