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On the rectilinear art gallery problem algorithmic aspects

  • Computational Geometry
  • Conference paper
  • First Online:
Graph-Theoretic Concepts in Computer Science (WG 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 484))

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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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Rolf H. Möhring

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© 1991 Springer-Verlag Berlin Heidelberg

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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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