Guarding orthogonal art galleries with sliding cameras

Matthew J. Katz; Gila Morgenstern

doi:10.1142/S0218195911003639

Guarding orthogonal art galleries with sliding cameras

Matthew J. Katz
, Gila Morgenstern

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

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 2-approximation can be found in polynomial time for x-monotone galleries.

Original language	English
Pages (from-to)	241-250
Number of pages	10
Journal	International Journal of Computational Geometry and Applications
Volume	21
Issue number	2
DOIs	https://doi.org/10.1142/S0218195911003639
State	Published - 1 Apr 2011

Keywords

Art-gallery
link distance
mobile guards
orthogonal polygons
perfect graphs

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

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10.1142/S0218195911003639

Cite this

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abstract = "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 2-approximation can be found in polynomial time for x-monotone galleries.",

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AB - 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 2-approximation can be found in polynomial time for x-monotone galleries.

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KW - mobile guards

KW - orthogonal polygons

KW - perfect graphs

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Guarding orthogonal art galleries with sliding cameras

Abstract

Keywords

ASJC Scopus subject areas

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