The prison yard problem


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.

This is a preview of subscription content, access via your institution.


  1. [1]

    A. Aggarwal:The Art Gallery Theorem: Its Variations, Applications and Algorithmic Aspects, Ph. D. Thesis, The Johns Hopkins University, Baltimore, Maryland, 1984.

    Google Scholar 

  2. [2]

    V. Chvátal: A combinatorial theorem in plane geometry,Journal of Combinatorial Theory, Ser. B 18 (1975), 39–41.

    Google Scholar 

  3. [3]

    M. M. Klawe, J. Kahn, andL. A. Kleitman: Traditional galleries require fewer watchman,SIAM J. of Algebraic and Discrete Methods 4 (1983), 194–206.

    Google Scholar 

  4. [4]

    V. Klee, 1973. See [7]—.

    Google Scholar 

  5. [5]

    A. A. Kooshesh, B. M. E. Moret, andL. A. Székely: Improved bounds for the prison yard problem,Proceedings of the 21st southeastern international conference on combinatorics, graph theory and computing (Boca Raton, Fla., 1990)Congressus Numerantium 76 (1990), 145–149.

    Google Scholar 

  6. [6]

    D. T. Lee, andA. K. Lin: Computational complexity of art gallery problems,IEEE Trans. Inf. Theory 32 (1986), 276–282.

    Google Scholar 

  7. [7]

    J. O'Rourke:Art Gallery Theorems and Algorithms, Oxford University Press, New York, 1987.

    Google Scholar 

  8. [8]

    T. Shermer: Recent results in art galleries,Proc. IEEE, 1992.

  9. [9]

    Mamoru Watanabe: A few problems related to the art gallery problems,manuscript 1990.

Download references

Author information



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

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Füredi, Z., Kleitman, D.J. The prison yard problem. Combinatorica 14, 287–300 (1994).

Download citation

AMS subject classification code (1991)

  • 52 A 30