LATIN 2014: LATIN 2014: Theoretical Informatics pp 294-305

A (7/2)-Approximation Algorithm for Guarding Orthogonal Art Galleries with Sliding Cameras

• Stephane Durocher
• Omrit Filtser
• Robert Fraser
• Ali D. Mehrabi
• Saeed Mehrabi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)

Abstract

Consider a sliding camera that travels back and forth along an orthogonal line segment s inside an orthogonal polygon P with n vertices. The camera can see a point p inside P if and only if there exists a line segment containing p that crosses s at a right angle and is completely contained in P. In the minimum sliding cameras (MSC) problem, the objective is to guard P with the minimum number of sliding cameras. In this paper, we give an O(n 5/2)-time (7/2)-approximation algorithm to the MSC problem on any simple orthogonal polygon with n vertices, answering a question posed by Katz and Morgenstern (2011). To the best of our knowledge, this is the first constant-factor approximation algorithm for this problem.

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Authors and Affiliations

• Stephane Durocher
• 1
• Omrit Filtser
• 2
• Robert Fraser
• 1
• Ali D. Mehrabi
• 3
• Saeed Mehrabi
• 1
1. 1.Department of Computer ScienceUniversity of ManitobaCanada
2. 2.Department of Computer ScienceBen-Gurion University of the NegevIsrael
3. 3.Department of Mathematics and Computer ScienceEindhoven University of TechnologyThe Netherlands