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Shortest Path to View a Point in General Polygons

Narenji Sheshkalani, Ali | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44648 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Ghodsi, Mohammad; Abam, Mohammad Ali
  7. Abstract:
  8. We consider two variations of shortest paths problem inside a poly-gon. In the first variation, we want to find a shortest path from asource to view a destination inside a polygon with holes. We pro-pose two algorithms for this problem with the time complexity of O (hn log n) and O(n log n) in which the second one is optimal. In the second variation, we want to place a center policeman inside a sim-ple polygon so that the longer of the two shortest paths from two existing guards to the visibility polygon of the center policeman is minimized. We propose an algorithm for this problem with the time complexity of O(n 3)
  9. Keywords:
  10. Shortest Path ; Computational Geometry ; Visibility Algorithm