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International Conference on Vector and Parallel Processing

International Conference on Parallel Processing

VAPP 1994, CONPAR 1994: Parallel Processing: CONPAR 94 — VAPP VI pp 371–380Cite as

Parallel heap construction using multiple selection

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 854))

Abstract

We consider the problem of constructing data structures that implement priority queues (viz. the heap) and double-ended priority queues (namely, the twin-heap, the min-max heap, and the deap) quickly and optimally in parallel. Whereas all these heap-like structures can be built in linear sequential time, we show in this paper that the construction problem can be solved in O(log n·log* n/log log n) time using n·log log n/log n·log * n processors in the Arbitrary CRCW PRAM model. Moreover, by applying random sampling techniques, we reduce the construction time to O with probability ≥ 1−n−c for some constant c>0. As a by-product, we also investigate the parallel complexity of the multiple selection problem. The problem is to select a subset of elements having specified ranks from a given set. We design optimal solutions to the problem with respect to various models of parallel computation.

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References

  1. A. V. Aho, J. E. Hopocroft, and J. D. Ullman: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Massachusetts, 1974.

    Google Scholar 

  2. S. G. Akl: The Design and Analysis of Parallel Algorithms. Prentice-Hall, Englewood Cliffs, New Jersey, 1989.

    Google Scholar 

  3. M. D. Atkinson, J.-R. Sack, N. Santoro, and Th. Strothotte: Min-max heaps and generalized priority queues. Communications of the ACM 29 (10) (1986), 996–1000.

    Google Scholar 

  4. Y. Azar and N. Pippenger: Parallel selection. Discrete Applied Mathematics 27 (1–2) (1990), 49–58.

    Google Scholar 

  5. M. Blum, R. W. Floyd, V. Pratt, R. L. Rivest, and R. E. Tarjan: Time bounds for selection. Journal of Computer and System Sciences 7 (4) (1973), 448–461.

    Google Scholar 

  6. R. P. Brent: The parallel evaluation of general arithmetic expressions. Journal of the ACM 21 (2) (1974), 201–206.

    Google Scholar 

  7. S. Carlsson: The deap — A double-ended heap to implement double-ended priority queues. Information Processing Letters 26 (1) (1987), 33–36.

    Google Scholar 

  8. S. Carlsson and J. Chen: Parallel constructions of heaps and min-max heaps. Parallel Processing Letters 2 (4) (1992), 311–320.

    Google Scholar 

  9. J. Chen: Constructing priority queues and deques optimally in parallel. Proceedings of the Twelfth World Computer Congress, Volume I, (J. van Leeuwen, Ed.) Madrid, Spain (1992), 275–283.

    Google Scholar 

  10. R. J. Cole: An optimally efficient selection algorithm. Information Processing Letters 26 (1987/88) 295–299.

    Google Scholar 

  11. R. J. Cole: Parallel merge sort. SIAM Journal on Computing 17 (1988) 770–785.

    Google Scholar 

  12. R. J. Cole and U. Vishkin: Faster optimal prefix sums and list ranking. Information and Control 81 (1989) 334–352.

    Google Scholar 

  13. P. F. Dietz: Heap construction in the parallel comparison tree model. In: Proceedings of the 3rd Scandinavian Workshop on Algorithm Theory (1992), 140–150.

    Google Scholar 

  14. R. W. Floyd: Algorithm 245 — Treesort 3. Communications of the ACM 7 (12) (1964), 701.

    Google Scholar 

  15. R. W. Floyd and R. L. Rivest: Expected time bounds for selection. Communications of the ACM 18 (1975) 165–172.

    Google Scholar 

  16. M. L. Fredman and T. H. Spencer: Refined complexity analysis for heap operations. Journal of Computer and System Sciences 35 (3) (1987), 269–284.

    Google Scholar 

  17. G. H. Gonnet and J. I. Munro: Heaps on heaps. SIAM Journal on Computing 15 (4) (1986), 964–971.

    Google Scholar 

  18. D. E. Knuth: The Art of Computer Programming. Vol. 3: Sorting and Searching. Addison-Wesley, Reading, Massachusetts, 1973.

    Google Scholar 

  19. S. Rajasekaran and J. H. Reif: Derivation of randomized sorting and selection algorithms. Technical Report, Aiken Computing Lab., Harvard University, 1987.

    Google Scholar 

  20. N. S. V. Rao and W. Zhang: Building heaps in parallel. Information Processing Letters 37 (1991) 355–358.

    Google Scholar 

  21. Th. Strothotte, P. Eriksson, and S. Vallner: A note on constructing min-max heaps. BIT 29 (2) (1989), 251–256.

    Google Scholar 

  22. L. G. Valiant: Parallelism in comparison problems. SIAM Journal on Computing 4 (1975) 348–355.

    Google Scholar 

  23. J. W. J. Williams: Algorithm 232: Heapsort. Communications of the ACM 7 (6) (1964), 347–348.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Luleå University, S-971 87, Luleå, Sweden

    Jingsen Chen

Authors
  1. Jingsen Chen
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Editor information

Bruno Buchberger Jens Volkert

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© 1994 Springer-Verlag Berlin Heidelberg

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Chen, J. (1994). Parallel heap construction using multiple selection. In: Buchberger, B., Volkert, J. (eds) Parallel Processing: CONPAR 94 — VAPP VI. VAPP CONPAR 1994 1994. Lecture Notes in Computer Science, vol 854. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58430-7_33

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  • DOI: https://doi.org/10.1007/3-540-58430-7_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58430-8

  • Online ISBN: 978-3-540-48789-0

  • eBook Packages: Springer Book Archive

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