Guard Placement in Rectilinear Polygons

Jörg Rüdiger Sack, Godfried T. Toussaint

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Guard placement problems have been extensively studied by mathematicians as well as computer scientists. The classical guard problem posed by Victor Klee is to determine the number of guards sufficient to see any art gallery given as an n-vertex simple polygon. Here we study traditional (or rectilinear) art-galleries, i.e. galleries in which all interior angles are either 270° or 90°. The Rectilinear Art Gallery Theorem originally proved by Kahn, Klawe and Kleitman states that any n-vertex rectilinear art gallery can always be guarded by at most [n/4 J guards. Here we examine the problem from its computational point-of-view by providing an algorithmic proof of the Rectilinear Art Gallery Theorem. It is demonstrated that guard placement in monotone rectilinear polygons can be done in linear time, while the problem can be solved for arbitrary, nvertex, rectilinear polygons in 0 ( n loglog n) time.

Original languageEnglish (US)
Title of host publicationMachine Intelligence and Pattern Recognition
Pages153-175
Number of pages23
EditionC
DOIs
StatePublished - Jan 1 1988

Publication series

NameMachine Intelligence and Pattern Recognition
NumberC
Volume6
ISSN (Print)0923-0459

ASJC Scopus subject areas

  • Computer Vision and Pattern Recognition
  • Artificial Intelligence

Cite this

Sack, J. R., & Toussaint, G. T. (1988). Guard Placement in Rectilinear Polygons. In Machine Intelligence and Pattern Recognition (C ed., pp. 153-175). (Machine Intelligence and Pattern Recognition; Vol. 6, No. C). https://doi.org/10.1016/B978-0-444-70467-2.50016-3