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Mobile versus Point Guards

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.

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Correspondence to Tamás Róbert Mezei.

Additional information

Ervin Győri—Research of the authors was supported by NKFIH grant K-116769.

Editor in Charge: János Pach

Appendix A Linear Time Algorithm for MHSC

Appendix A Linear Time Algorithm for MHSC

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Győri, E., Mezei, T.R. Mobile versus Point Guards. Discrete Comput Geom 61, 421–451 (2019). https://doi.org/10.1007/s00454-018-9996-x

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Keywords

  • Art gallery problem
  • Orthogonal polygon
  • Mobile guard
  • Sliding cameras

Mathematics Subject Classification

  • 52C15
  • 68R05
  • 68U05