Heap construction in the parallel comparison tree model
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.
KeywordsPriority Queue Deterministic Algorithm Sequential Algorithm Parallel Selection Pram Model
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- Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, New York, 1974.Google Scholar
- 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
- 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
- Y. Azar and N. Pippenger. Parallel selection. Discrete Appl. Math., 27:49–58, 1990.Google Scholar
- 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
- 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
- Y. Matias O. Berkman and U. Vishkin, July 1991. Unpublished manuscript.Google Scholar
- N. S. V. Rao and W. Zhang. Building heaps in parallel. Info. Proc. Lett., 37:355–358, 1991.Google Scholar
- Rüdiger Reischuk. Probabilistic parallel algorithms for sorting and selection. SIAM J. On Computing, 14(2):396–409, May 1985.Google Scholar
- Leslie G. Valiant. Parallelism in comparison problems. SIAM J. On Computing, 4(3):348–355, September 1975.Google Scholar
- Uzi Vishkin. Structural parallel algorithmics. In ICALP 91, pages 363–380, July 1991.Google Scholar