Guarding rectangular art galleries

J. Czyzowicz; E. Rivera-Campo; N. Santoro; J. Urrutia; J. Zaks

doi:10.1016/0166-218X(92)00029-L

Guarding rectangular art galleries

J. Czyzowicz, E. Rivera-Campo, N. Santoro, J. Urrutia, J. Zaks

Department of Mathematics

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

Abstract

Consider a rectangular art gallery divide into n rectangular rooms, such that any two rooms sharing a wall in common have a door connecting them. How many guards need to be stationed in the gallery so as to protect all of the rooms in our gallery? Note that of a guard is stationed at a door, he will be able to guard two rooms. Our main aim in this paper is to show that ⌈n/2⌉ guards are always sufficient to protect all rooms in a rectangular art gallery. Extensions of our result are obtained for non-rectangular galleries and for 3-dimensional art galleries.

Original language	English
Pages (from-to)	149-157
Number of pages	9
Journal	Discrete Applied Mathematics
Volume	50
Issue number	2
DOIs	https://doi.org/10.1016/0166-218X(92)00029-L
State	Published - 6 May 1994

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/0166-218X(92)00029-L

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AU - Santoro, N.

AU - Urrutia, J.

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AB - Consider a rectangular art gallery divide into n rectangular rooms, such that any two rooms sharing a wall in common have a door connecting them. How many guards need to be stationed in the gallery so as to protect all of the rooms in our gallery? Note that of a guard is stationed at a door, he will be able to guard two rooms. Our main aim in this paper is to show that ⌈n/2⌉ guards are always sufficient to protect all rooms in a rectangular art gallery. Extensions of our result are obtained for non-rectangular galleries and for 3-dimensional art galleries.

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Guarding rectangular art galleries

Abstract

ASJC Scopus subject areas

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