The prison yard problem

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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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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AMS subject classification code (1991)

  • 52 A 30