A range minima parallel algorithm for coarse grained multicomputers

  • H. Mongelli
  • S. W. Song
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1586)

Abstract

Given an array of n real numbers A=(a1, a2, ..., an), define MIN(i, j) = min {ai, ..., aj}. The range minima problem consists of preprocessing array A such that queries MIN(i,j), for any 1≤ijn, can be answered in constant time. Range minima is a basic problem that appears in many other important problems such as lowest common ancestor, Euler tour, pattern matching with scaling, etc. In this work we present a parallel algorithm under the CGM model (Coarse Grained Multicomputer), that solves the range minima problem in O(n/p) time and constant number of communication rounds.

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References

  1. 1.
    A. V. Aho, J. E. Hopcroft, and J.D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley Publishing Company, 1975.Google Scholar
  2. 2.
    N. Alon and B. Schieber. Optimal preprocessing for answering on-line product queries. Technical Report TR 71/87, The Moise and Frida Eskenasy Inst. of Computer Science, Tel Aviv University, 1987.Google Scholar
  3. 3.
    A. Amir, G. M. Landau, and U. Vishkin. Efficient pattern matching with scaling. Journal of Algorithms, 13:2–32, 1992.MATHCrossRefGoogle Scholar
  4. 4.
    O. Berkman, B. Schieber, and U. Vishkin. Optimal doubly logarithmic parallel algorithms based on finding all nearest smaller values. Journal of Algorithms, 14:344–370, 1993.MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    O. Berkman and U. Vishkin. Recursive star-tree parallel data structure. SIAM J. Comput., 22(2):221–242, 1993.MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    E. Cáceres, F. Dehne, A. Ferreira, P. Flocchini, I. Rieping, A. Roncato, N. Santoro, and S. W. Song. Efficient parallel graph algorithms for coarse grained multicomputers and BSP. In Proc. ICALP’97, 1997.Google Scholar
  7. 7.
    F. Dehne, A. Fabri, and C. Kenyon. Scalable and architecture independent parallel geometric algorithms with high probability optimal time. In Proc. 6th IEEE Symposium on Parallel and Distributed Processing, pages 586–593, 1994.Google Scholar
  8. 8.
    F. Dehne, A. Fabri, and A. Rau-Chaplin. Scalable parallel computational geometry for coarse grained multicomputers. In Proc. ACM 9th Annual Computational Geometry, pages 298–307, 1993.Google Scholar
  9. 9.
    F. Dehne and S. W. Song. Randomized parallel list ranking for distributed memory multiprocessors. In Proc. Second Asian Computing Science Conference (ASIAN’96), pages 1–10, 1996.Google Scholar
  10. 10.
    H. N. Gabow, J. L. Bentley, and R. E. Tarjan. Scaling and related techniques for geometry problems. In Proc. 16th ACM Symp. On Theory of Computing, pages 135–143, 1984.Google Scholar
  11. 11.
    D. Harel and R. E. Tarjan. Fast algorithms for finding nearest common ancestors. SIAM J. Comput., 13(2):338–335, 1984.MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    J. Jájá. An Introduction to Parallel Algorithms. Addison-Wesley Publishing Company, 1992.Google Scholar
  13. 13.
    R. Lin and S. Olariu. A simple optimal parallel algorithm to solve the lowest common ancestor problem. In Proc. of International Conference on Computing and Information-ICCI’91, number 497 in Lecture Notes in Computer Science, pages 455–461, 1991.Google Scholar
  14. 14.
    V. L. Ramachandran and U. Vishkin. Efficient parallel triconectivity in logarithmic parallel time. In Proc. of AWOC’88, number 319 in Lecture Notes in Computer Science, pages 33–42, 1988.Google Scholar
  15. 15.
    J. H. Reif, editor. Synthesis of Parallel Algorithms. Morgan Kaufmann Publishers, 1993.Google Scholar
  16. 16.
    B. Schieber and U. Vishkin. On finding lowest common ancestors: simplification and parallelization. SIAM J. Comput., 17:1253–1262, 1988.MATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    L. G. Valiant. A bridging model for parallel computation. Comm. of the ACM, 33:103–111, 1990.CrossRefGoogle Scholar
  18. 18.
    J. Vuillemin. A unified look at data structures. Comm. of the ACM, 23:229–239, 1980.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • H. Mongelli
    • 1
  • S. W. Song
    • 2
  1. 1.Universidade Federal do mato Grosso do Sul and Universidade de São PauloSao PauloBrazil
  2. 2.Universidade de São PauloSao PauloBrazil

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