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Enclosing many boxes by an optimal pair of boxes

  • Bruno Becker
  • Paolo Giulio Franciosa
  • Stephan Gschwind
  • Thomas Ohler
  • Gerald Thiemt
  • Peter Widmayer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)

Abstract

We look at the problem: Given a set M of n d- dimensional intervals, find two d-dimensional intervals S, T, such that all intervals in M are enclosed by S or by T, the distribution is balanced and the intervals S and T fulfill a geometric criterion, e.g. like minimum area sum. Up to now no polynomial time algorithm was known for that problem. We present an O(dn log n + d2n2d 1) algorithm for finding an optimal solution.

Keywords

computational geometry covering problems axis-parallel rectangles 

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References

  1. [AIKS89]
    A. Aggarwal, H. Imai, N. Katoh, and S. Suri. Finding k points with minimum diameter and related problems. Proc. of the 5th Annual ACM Symposium on Computational Geometry, 5:283–291, 1989.Google Scholar
  2. [BFG+91]
    B. Becker, P. G. Franciosa, S. Gschwind, T. Ohler, G. Thiemt, and P. Widmayer. An optimal algorithm for approximating a set of rectangles by two minimum area rectangles. In 7th Workshop on Computational Geometry, Bern, Lecture Notes in Computer Science, page to appear, 1991.Google Scholar
  3. [BKSS90]
    N. Beckmann, H.P. Kriegel, R. Schneider, and B. Seeger. The r*-tree: An efficient and robust access method for points and rectangles. ACM SIGMOD International Conf. on Management of Data, 19:322–331, 1990.Google Scholar
  4. [Gre89]
    D. Greene. An implementation and performance analysis of spatial access methods. Fifth IEEE International Conference on Data Engineering, Los Angeles, 5:606–615, 1989.Google Scholar
  5. [Gut84]
    A. Guttman. R-trees: A dynamic index structure for spatial searching. ACM SIGMOD International Conf. on Management of Data, 12:47–57, 1984.Google Scholar
  6. [PS85]
    F. P. Preparata and M. I. Shamos. Computational Geometry, an Introduction. Springer-Verlag, New York, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Bruno Becker
    • 1
  • Paolo Giulio Franciosa
    • 2
  • Stephan Gschwind
    • 1
  • Thomas Ohler
    • 1
  • Gerald Thiemt
    • 1
  • Peter Widmayer
    • 1
  1. 1.Institut für InformatikUniversität FreiburgFreiburg
  2. 2.Dipartimento di Informatica e SistemisticaUniversità “La Sapienza”RomaItaly

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