Guarding Orthogonal Polygons with Sliding Cameras

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Seddighin, Saeed Reza | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 45234 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Ghodsi, Mohammad
Abstract:
In this research, we consider the problem of guarding orthogonal polygon with sliding cameras. This problem is originated from the well-known Art Gallery problem. In the Art Gallery problem the goal is to guard the polygon with minimum number of guards. Each guard is considered as a point and can guard all the points inside the polygon that are in its visibility area. In sliding camera version, each guard is modeld as a horizontal or vertical segment which is entirely in the polygon. The guarding area of each camera is defined by its segment and its power. In 0-transmitter model, the guarding area of each camera is limited by the edges of polygon, but in the k-transmitter model cameras can see through k edges.The goal of the problem can be defined as minimizing the number of guards, or minimizing the total sum of the length of cameras. In this research we show that some of the problems have polynomial time solutions, while the others are NP-hard. We also give approximation algorithms for some versions of the roblems
Keywords:
Algorithm ; Computational Geometry ; Guarding Polygons ; Sliding Cameras