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Algorithmica

, Volume 15, Issue 2, pp 154–171 | Cite as

Optimal cooperative search in fractional cascaded data structures

  • R. Tamassia
  • J. S. Vitter
Article

Abstract

Fractional cascading is a technique designed to allow efficient sequential search in a graph with catalogs of total sizen. The search consists of locating a key in the catalogs along a path. In this paper we show how to preprocess a variety of fractional cascaded data structures whose underlying graph is a tree so that searching can be done efficiently in parallel. The preprocessing takesO(logn) time withn/logn processors on an EREW PRAM. For a balanced binary tree, cooperative search along root-to-leaf paths can be done inO((logn)/logp) time usingp processors on a CREW PRAM. Both of these time/processor constraints are optimal. The searching in the fractional cascaded data structure can be either explicit, in which the search path is specified before the search starts, or implicit, in which the branching is determined at each node. We apply this technique to a variety of geometric problems, including point location, range search, and segment intersection search.

Key words

Parallel computing Fractional cascading PRAM Search Cooperative search Point location Computational geometry 

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References

  1. [1]
    M. J. Atallah, R. Cole, and M. T. Goodrich. Cascading divide-and-conquer: a technique for designing parallel algorithms.SIAM J. Comput., 18:499–532, 1989.Google Scholar
  2. [2]
    B. Chazelle. How to search in history.Inform. Control, 64:77–99, 1985.Google Scholar
  3. [3]
    B. Chazelle and L. J. Guibas. Fractional cascading: I. A data structuring technique.Algorithmica, 1:133–162, 1986.Google Scholar
  4. [4]
    B. Chazelle and L. J. Guibas. Fractional cascading: II. Applications.Algorithmica, 1:163–191, 1986.Google Scholar
  5. [5]
    K. L. Clarkson, R. Cole, and R. E. Tarjan. Erratum: Randomized parallel algorithms for trapezoidal diagrams.Internat. J. Comput. Geom. Appl., 2(3):341–343, 1992.Google Scholar
  6. [6]
    K. L. Clarkson, R. Cole, and R. E. Tarjan. Randomized parallel algorithms for trapezoidal diagrams.Internat. J. Comput. Geom. Appl., 2(2):117–133, 1992.Google Scholar
  7. [7]
    N. Dadoun and D. G. Kirkpatrick. Cooperative subdivision search algorithms with applications.Proc. 27th Allerton Conf. on Communication, Control, and Computing, pp. 538–547, 1989.Google Scholar
  8. [8]
    M. Edahiro, I. Kokubo, and Ta. Asano. A new point-location algorithm and its practical efficiency: comparison with existing algorithms.ACM Trans. Graph., 3:86–109, 1984.Google Scholar
  9. [9]
    H. Edelsbrunner, L. J. Guibas, and J. Stolfi. Optimal point location in a monotone subdivision.SIAM J. Comput., 15:317–340, 1986.Google Scholar
  10. [10]
    M. T. Goodrich. Triangulating a polygon in parallel.J. Algorithms, 10:327–351, 1989.Google Scholar
  11. [11]
    M. T. Goodrich. Planar separators and parallel polygon triangulation.Proc. 24th ACM Symp. on Theory of Computing, pp. 507–516, 1992.Google Scholar
  12. [12]
    D. G. Kirkpatrick. Optimal search in planar subdivisions.SIAM J. Comput., 12:28–35, 1983.Google Scholar
  13. [13]
    D. T. Lee and F. P. Preparata. Location of a point in a planar subdivision and its applications.SIAM J. Comput., 6:594–606, 1977.Google Scholar
  14. [14]
    K. Mehlhorn and S. Näher. Dynamic fractional cascading.Algorithmica, 5:215–241, 1990.Google Scholar
  15. [15]
    F. P. Preparata and M. I. Shamos.Computational Geometry: an Introduction. Springer-Verlag, New York, 1985.Google Scholar
  16. [16]
    M. Snir. On parallel searching.SIAM J. Comput., 14(3):688–708, 1989.Google Scholar
  17. [17]
    R. Tamassia and J. S. Vitter. Parallel transitive closure and point location in planar structures.SIAM J. Comput., 20(4):708–725, 1991.Google Scholar
  18. [18]
    C. K. Yap. Parallel triangulation of a polygon in two calls to the trapezoidal map.Algorithmica, 3:279–288, 1988.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1996

Authors and Affiliations

  • R. Tamassia
    • 1
  • J. S. Vitter
    • 2
  1. 1.Department of Computer ScienceBrown UniversityProvidenceUSA
  2. 2.Department of Computer ScienceDuke UniversityDurhamUSA

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