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Mobile versus Point Guards

  • Ervin Győri
  • Tamás Róbert Mezei
Article

Abstract

We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using “rectangular vision”. We prove a sharp bound on the minimum number of point guards required to cover the gallery in terms of the minimum number of vertical mobile guards and the minimum number of horizontal mobile guards required to cover the gallery. Furthermore, we show that the latter two numbers can be computed in linear time.

Keywords

Art gallery problem Orthogonal polygon Mobile guard Sliding cameras 

Mathematics Subject Classification

52C15 68R05 68U05 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Alfréd Rényi Institute of Mathematics, Hungarian Academy of SciencesBudapestHungary
  2. 2.Department of Mathematics and Its ApplicationsCentral European UniversityBudapestHungary

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