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Mobile versus Point Guards

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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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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13–15, Budapest, 1053, Hungary

    Ervin Győri & Tamás Róbert Mezei

  2. Department of Mathematics and Its Applications, Central European University, Nádor u. 9, Budapest, 1051, Hungary

    Ervin Győri & Tamás Róbert Mezei

Authors
  1. Ervin Győri
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  2. Tamás Róbert Mezei
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Correspondence to Tamás Róbert Mezei.

Additional information

Editor in Charge: János Pach

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

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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  • DOI: https://doi.org/10.1007/s00454-018-9996-x

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