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A lower bound and two approximative algorithms for the K-partitioning of rectilinear polygons

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SWAT 88 (SWAT 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 318))

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Abstract

This paper is about partitions that decompose a rectilinear polygon with n vertices (an n-gon) into rectilinear polygons with no more than k vertices each, where k is given and k<n. First we prove a lower bound L(P,k) for the number of components in the k-partition of a given n-gon P. Then two heuristic algorithms for the k-partitioning problem are presented. Their time complexities are O(n log2 n) or O(n 2log n), depending on the properties of the given n-gon. In most cases, both algorithms find k-partitions with no more than 2L(P,k) components.

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References

  1. Edelsbrunner, H., O'Rourke, J., and Welzl, E., "Stationing Guards in Rectilinear Art Galleries", Comp. Vision, Graphics, and Image Proc. Vol.27, 1984.

    Google Scholar 

  2. Günther, O., "Partitioning Algorithms for Rectilinear Polygons", Diplomarbeit, Universität Karlsruhe, West Germany, 1984.

    Google Scholar 

  3. Günther, O., "Algorithms for the Minimum K-Partitioning of Rectilinear Polygons", Proc. 23rd Annual Allerton Conference on Communication, Control and Computing, 1985.

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  4. Lee, D.T. and F.P. Preparata, "Location of a Point in a Planar Subdivision and its Applications", SIAM J. Comp., Vol. 6, No. 3, 1977.

    Google Scholar 

  5. Lodi, E., Luccio, F., Mugnai, C., Pagli, L., and Lipski, W., "On Two-dimensional Data Organization II", Fundamenta Informaticae, Vol. 2, No. 3, 1979.

    Google Scholar 

  6. Ohtsuki, T., "Minimum Dissection of Rectilinear Regions", Proc. IEEE Int. Symp. on Circuits and Systems, 1982.

    Google Scholar 

  7. Sack, J.R., "An O(n log n) Algorithm for Decomposing Simple Rectilinear Polygons into Convex Quadrilaterals", Proc. 20th Annual Allerton Conference on Communication, Control and Computing, 1982.

    Google Scholar 

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Authors and Affiliations

  1. International Computer Science Institute, 1947 Center St., Suite 600, 94704, Berkeley, CA

    Oliver Günther

Authors
  1. Oliver Günther
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Editor information

Rolf Karlsson Andrzej Lingas

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© 1988 Springer-Verlag Berlin Heidelberg

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Günther, O. (1988). A lower bound and two approximative algorithms for the K-partitioning of rectilinear polygons. In: Karlsson, R., Lingas, A. (eds) SWAT 88. SWAT 1988. Lecture Notes in Computer Science, vol 318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19487-8_9

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  • DOI: https://doi.org/10.1007/3-540-19487-8_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19487-3

  • Online ISBN: 978-3-540-39288-0

  • eBook Packages: Springer Book Archive

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