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The prison yard problem

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Abstract

Given a polygon II withn vertices whose sides arewalls. Guards, located at vertices can see all directions, but cannot see beyond walls. We prove that at most [n/2] guards suffice to see everywhere the whole plane. If II is not convex, then [n/2] suffice.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois, 61801-2917, Urbana, IL, USA

    Zoltán Füredi

  2. Mathematical Institute of the, Hungarian Academy of Sciences, P.O.B. 127, 1364, Budapest, Hungary

    Zoltán Füredi

  3. Deptartment of Mathematics, Massachusetts Institute of Technology, 02139-4307, Cambridge, MA, USA

    D. J. Kleitman

Authors
  1. Zoltán Füredi
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  2. D. J. Kleitman
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Additional information

The research was done while this author visited the Department of Mathematics at Rutgers University. Research supported in part by the Hungarian National Science Foundation under grant No. 1812

Supported in part by NSF grant DMS 86-06225 and AF grant OSR-86-0078

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Füredi, Z., Kleitman, D.J. The prison yard problem. Combinatorica 14, 287–300 (1994). https://doi.org/10.1007/BF01212977

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  • DOI: https://doi.org/10.1007/BF01212977

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