Tight bounds for the rectangular art gallery problem

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Consider a rectangular art gallery, subdivided into n rectangular rooms; any two adjacent rooms have a door connecting them. We show that ⌈n/2⌉ guards are always sufficient to protect all rooms in a rectangular art gallery; furthermore, their positioning can be determined in O(n) time. We show that the optimal positioning of the guards can be determined in linear time. We extend the result by proving that in an arbitrary orthogonal art gallery (not necessarily convex, possibly having holes) with n rectangular rooms and k walls, ⌈(n+k)/2⌉ guards are always sufficient and occasionally necessary to guard all the rooms in our gallery. A linear time algorithm to find the positioning of the guards is obtained.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 17th International Workshop, WG 1991, Proceedings
EditorsGunther Schmidt, Rudolf Berghammer
PublisherSpringer Verlag
Number of pages8
ISBN (Print)9783540551218
StatePublished - 1992
Event17th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1991 - Fischbachau, Germany
Duration: 17 Jun 199119 Jun 1991

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume570 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 1991

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1992.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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