Guarding orthogonal art galleries with sliding cameras

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Guarding orthogonal art galleries with sliding cameras

Let P be an orthogonal polygon with n vertices. A sliding camera travels back and forth along an orthogonal line segment s ⊆ P corresponding to its trajectory. The camera sees a point p ∈ P if there is a point q ∈ s such that pq is a line segment normal to s that is completely contained in P . In the MinimumCardinality Sliding Cameras (MCSC) problem, the objective is to find a set S of sliding ...

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Guarding Orthogonal Art Galleries with Sliding Cameras

We study the problem of guarding an orthogonal art gallery with security cameras sliding back and forth along straight tracks. We show that if only vertical (alternatively, horizontal) tracks are allowed, then a solution minimizing the number of tracks can be found in polynomial time, and if both orientations are allowed, then a 3-approximation can be found in polynomial time.

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A sliding camera travelling along a line segment s in a polygon P can see a point p in P if and only if p lies on a line segment contained in P that intersects s at a right angle. The objective of the minimum sliding cameras (MSC) problem is to guard P with the fewest sliding cameras possible, each of which is a horizontal or vertical line segment. In this paper, we give an O(n)-time 3-approxim...

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ژورنال

عنوان ژورنال: Computational Geometry

سال: 2017

ISSN: 0925-7721

DOI: 10.1016/j.comgeo.2017.04.001