Shortest Path to View a Point in General Polygons, M.Sc. Thesis Sharif University of Technology ; Ghodsi, Mohammad (Supervisor) ; Abam, Mohammad Ali (Co-Advisor)
Abstract
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)
Cataloging briefShortest Path to View a Point in General Polygons, M.Sc. Thesis Sharif University of Technology ; Ghodsi, Mohammad (Supervisor) ; Abam, Mohammad Ali (Co-Advisor)
Abstract
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)
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