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On the rectilinear art gallery problem

  • Frank Hoffmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 443)

Abstract

It is shown that [n/4] point guards are always sufficient and sometimes necessary to watch a rectilinear polygon with an arbitrary number of holes, where n is the total number of vertices.

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References

  1. [1]
    E. Györi, A short proof of the rectilinear art gallery theorem, SIAM J. Alg. Disc. Math. 7 (1986), 452–454Google Scholar
  2. [2]
    F. Hoffmann, On the rectilinear art gallery problem, Technical Report 89-5, DIMACS Center, Rutgers UniversityGoogle Scholar
  3. [3]
    F. Hoffmann, M. Kaufmann, On the rectilinear art gallery — algorithmic aspects, draft, March 1990Google Scholar
  4. [4]
    F. Hoffmann, K. Kriegel, Embedding rectilinear graphs in linear time, IPL 29 (1988), 75–79Google Scholar
  5. [5]
    J. Kahn, M. Klawe, D. Kleitmann, Traditional galleries require fewer watchmen, SIAM J. Alg. Disc. Math. 4 (1983), 194–206Google Scholar
  6. [6]
    R. Motwani, A Raghunathan, H. Saran, Covering orthogonal polygons with star polygons: The perfect graph approach, Proc. 4th ACM Symp. on Comp. Geometry 1988, 211–223Google Scholar
  7. [7]
    S. Ntafos, On gallery watchmen in grids, IPL 23 (1986), 99–102Google Scholar
  8. [8]
    J. O'Rourke, An alternate proof of the rectilinear art gallery theorem, J. on Geometry 21 (1983), 118–130Google Scholar
  9. [9]
    J. O'Rourke, Art gallery theorems and algorithms, Oxford Univ. Press. New York, 1987Google Scholar
  10. [10]
    W. Wessel, personal communication, 1989Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Frank Hoffmann
    • 1
  1. 1.Karl-Weierstraß-Institut für MathematikAkademie der Wissenschaften der DDRBerlin

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