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On the rectilinear art gallery problem algorithmic aspects

  • Frank Hoffmann
  • Michael Kaufmann
Computational Geometry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 484)

Abstract

We investigate the watchman problem for rectilinear art galleries with an arbitrary number of holes. An efficient algorithm for the placement of the guards with running time O(n3/2 log2n log log n) is presented. Each guard has to watch an r-star of constant size.

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References

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    E. Györi: “A short proof of the rectilinear art gallery theorem, SIAM J. Alg. Disc. Math. 7 (1986), 452–454.Google Scholar
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    F. Hoffmann: “On the rectilinear art gallery problem” Proc. ICALP'90, ed. M.Paterson, LNCS 443, pp. 717–728.Google Scholar
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    J. Kahn, M. Klawe, and D. Kleitman: “Traditional galleries require fewer watch-men”, SIAM Journal of Alg. Disc. Math. 4 (1983), 194–206.Google Scholar
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    K. Mehlhorn: “Data structures and algorithms” Vol. 3, Springer (1984)Google Scholar
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    J. O'Rourke: “Art gallery theorems and algorithms”, Oxford Univ. Press, New York, 1987.Google Scholar
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    J.R. Sack and G.T. Toussaint: “ Guard placement in rectilinear polygons” in “Computational Morphology”, edited by G.T. Toussaint, North-Holland 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Frank Hoffmann
    • 1
  • Michael Kaufmann
    • 2
  1. 1.Karl-Weierstraß-Institut für Mathematik der AdW der DDRBerlinFRG
  2. 2.FB 14, InformatikUniversität des SaarlandesSaarbrückenFRG

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