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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 1990: Graph-Theoretic Concepts in Computer Science pp 239–250Cite as

On the rectilinear art gallery problem algorithmic aspects

  • Computational Geometry
  • Conference paper
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Part of the book series: Lecture Notes in Computer Science ((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(n 3/2 log2 n log log n) is presented. Each guard has to watch an r-star of constant size.

Part of the research was done while the first author was visiting the Fachbereich Informatik, Universität des Saarlandes supported by a grant from DAAD. The second author was supported by a grant from DFG, SFB 124 VLSI-Entwurfsmethoden und Parallelität, B2.

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References

  1. E. Györi: “A short proof of the rectilinear art gallery theorem, SIAM J. Alg. Disc. Math. 7 (1986), 452–454.

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  2. F. Hoffmann: “On the rectilinear art gallery problem” Proc. ICALP'90, ed. M.Paterson, LNCS 443, pp. 717–728.

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  3. J. Kahn, M. Klawe, and D. Kleitman: “Traditional galleries require fewer watch-men”, SIAM Journal of Alg. Disc. Math. 4 (1983), 194–206.

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  4. K. Mehlhorn: “Data structures and algorithms” Vol. 3, Springer (1984)

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  5. J. O'Rourke: “Art gallery theorems and algorithms”, Oxford Univ. Press, New York, 1987.

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  6. J.R. Sack and G.T. Toussaint: “ Guard placement in rectilinear polygons” in “Computational Morphology”, edited by G.T. Toussaint, North-Holland 1988.

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Author information

Authors and Affiliations

  1. Karl-Weierstraß-Institut für Mathematik der AdW der DDR, Mohrenstraße 39, PF 1304, O-1086, Berlin, FRG

    Frank Hoffmann

  2. FB 14, Informatik, Universität des Saarlandes, W-6600, Saarbrücken, FRG

    Michael Kaufmann

Authors
  1. Frank Hoffmann
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  2. Michael Kaufmann
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Editor information

Rolf H. Möhring

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© 1991 Springer-Verlag Berlin Heidelberg

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Cite this paper

Hoffmann, F., Kaufmann, M. (1991). On the rectilinear art gallery problem algorithmic aspects. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1990. Lecture Notes in Computer Science, vol 484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53832-1_46

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  • DOI: https://doi.org/10.1007/3-540-53832-1_46

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53832-5

  • Online ISBN: 978-3-540-46310-8

  • eBook Packages: Springer Book Archive

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