Guarding art galleries by guarding witnesses

Authors:
Kyung-Yong Chwa;Byung-Cheol Jo;Christian Knauer;Esther Moet;René van Oostrum;Chan-Su Shin
Affiliations:
Department of Computer Science, KAIST, Daejon, Korea;Taff System, Co Ltd., Seoul, Korea;Freie Universität Berlin, Berlin, Germany;Institute of Information & Computing Sciences, Utrecht University, Utrecht, The Netherlands;Institute of Information & Computing Sciences, Utrecht University, Utrecht, The Netherlands;School of Electronics and Information Engineering, Hankuk University of Foreign Studies, Yongin, Korea
Venue:
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Year:
2004

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Abstract

Let P be a simple polygon We define a witness setW to be a set of points such that if any (prospective) guard set G guards W, then it is guaranteed that G guards P Not all polygons admit a finite witness set If a finite minimal witness set exists, then it cannot contain any witness in the interior of P; all witnesses must lie on the boundary of P, and there can be at most one witness in the interior of every edge We give an algorithm to compute a minimum witness set for P in O(n2log n) time, if such a set exists, or to report the non-existence within the same time bounds.