A pseudo-polynomial time O(log² n)-approximation algorithm for art gallery problems
Author(s)
Deshpande, Ajay A
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Other Contributors
Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Advisor
Sanjay E. Sarma.
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In this thesis, we give a pseudo-polynomial time O(log² n)-approximation algorithm for a variant of the art gallery problem the point-guard problem. The point-guard problem involves finding the minimum number of points and their positions so that guards located at these points cover the interior of the art gallery. Our algorithm is pseudo-polynomial in the sense that it is polynomial in the number of walls of the art gallery but is possibly exponential in the number of bits required to represent the positions of the vertices of the art gallery. Our approach involves reducing the point-guard problem to a new problem of choosing a minimum number of guard-locations from a finite set obtained by a special subdivision procedure. The new problem has the optimal solution at most three times the optional solution of the point-guard problem. We further reduce the new problem to the set cover problem and obtain an approximate solution to the set cover problem.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006. Includes bibliographical references (p. 55-56).
Date issued
2006Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Department of Mechanical EngineeringPublisher
Massachusetts Institute of Technology
Keywords
Mechanical Engineering., Electrical Engineering and Computer Science.