Heap construction in the parallel comparison tree model

  • Paul F. Dietz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 621)


I show how to put n values into heap order in O(log log n) time using n/ log log n processors in the parallel comparison tree model of computation, and in Õ(α(n)) time on n/α(n) processors, in the randomized parallel comparison tree model, where α(n) is an inverse of Ackerman's function. I prove similar bounds for the related problem of putting n values into a min-max heap.


Priority Queue Deterministic Algorithm Sequential Algorithm Parallel Selection Pram Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, New York, 1974.Google Scholar
  2. [2]
    M. Ajtai, J. Komlós, W. L. Steiger, and E. Szemerédi. Optimal parallel selection has complexity O(log log n). Journal of Computer and System Sciences, 38:125–133, 1989.Google Scholar
  3. [3]
    M. Atkinson, J. Sack, N. Santoro, and T. Strothotte. Min-max heaps and generalized priority queues. Communications of the ACM, 29(10):996–1000, October 1986.Google Scholar
  4. [4]
    Y. Azar and N. Pippenger. Parallel selection. Discrete Appl. Math., 27:49–58, 1990.Google Scholar
  5. [5]
    Omer Berkman and Uzi Vishkin. Recursive *-tree parallel data-structure. In Proc. 30th Ann. IEEE Symp. on Foundations of Computer Science, pages 196–202, October 1989.Google Scholar
  6. [6]
    Svante Carlsson and Jingsen Zhang. Parallel complexity of heaps and min-max heaps. Technical Report LU-CS-TR:91-77, Department of Computer Science, Lund University, Lund, Sweden, August 1991.Google Scholar
  7. [7]
    Y. Matias O. Berkman and U. Vishkin, July 1991. Unpublished manuscript.Google Scholar
  8. [8]
    N. S. V. Rao and W. Zhang. Building heaps in parallel. Info. Proc. Lett., 37:355–358, 1991.Google Scholar
  9. [9]
    Rüdiger Reischuk. Probabilistic parallel algorithms for sorting and selection. SIAM J. On Computing, 14(2):396–409, May 1985.Google Scholar
  10. [10]
    Leslie G. Valiant. Parallelism in comparison problems. SIAM J. On Computing, 4(3):348–355, September 1975.Google Scholar
  11. [11]
    Uzi Vishkin. Structural parallel algorithmics. In ICALP 91, pages 363–380, July 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Paul F. Dietz
    • 1
  1. 1.Department of Computer ScienceUniversity of RochesterRochester

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