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Optimal Parallel Initialization Algorithms for a Class of Priority Queues
October 1991 (vol. 2 no. 4)
pp. 423-429

An adaptive parallel algorithm for inducing a priority queue structure on an n-element array is presented. The algorithm is extended to provide optimal parallel construction algorithms for three other heap-like structures useful in implementing double-ended priority queues, namely min-max heaps, deeps, and min-max-pair heaps. It is shown that an n-element array can be made into a heap, a deap, a min-max heap, or a min-max-pairheap in O(log n+(n/p)) time using no more than n/log n processors, in the exclusive-read-exclusive-write parallel random-access machine model.

[1] M. D. Atkinson, J. R. Sack, N. Santoro, and T. Strothotte, "Min-max heaps and generalized priority queues,"Commun. ACM, vol. 29, pp. 996-1000, 1986.
[2] S. Baase,Computer Algorithms--An Introduction to Design and Analysis. Reading, MA: Addison-Wesley, 1988.
[3] J. Biswas and J. C. Browne, "Simultaneous update of priority structures," inProc. Int. Conf. Parallel Processing, 1987, pp. 124-131.
[4] S. Carlsson, "The deap--A double ended heap to implement double ended priority queues,"Inform. Processing Lett., vol. 26, pp. 33-36, 1987.
[5] S. Carlsson, J. Chen, and T. Strothotte, "A note on the construction of the data structure 'deap',"Inform. Processing Lett., vol. 31, pp. 315-317, 1989.
[6] E. G. Coffman and M. Hofri, "On scanning disks and the analysis of their steady state behavior," inProc. Conf. Measurement, Modelling Evaluating Com. Syst., New York, NY, Oct. 1982.
[7] N. Deo and S. Prasad, "Parallel heap," inProc. IEEE Int. Conf. Parallel Processing, 1990, pp. III-169-III-172.
[8] Z. Fan and K. H. Cheng, "A simultaneous access priority queue," inProc. Int. Conf. Parallel Processing, 1989, pp. I-95,I-98.
[9] M. Hofri, "Disk scheduling: FCFS versus SSTF revisited,"Commun. ACM, vol. 23, no. 11, pp. 645-653, Nov. 1980.
[10] G. H. Gonnet, "Heaps applied to event-driven mechanisms,"Commun. ACM, vol. 9, pp. 417-418, 1976.
[11] G. H. Gonnet and I. Munro, "Heaps on heaps,"SIAM J. Comput., vol. 15, pp. 964-971, 1986.
[12] A. Hasham and J. R. Sack, "Bounds for min-max heaps,"BIT, vol. 27 pp. 315-323, 1987.
[13] K. Hwang and F. A. Briggs,Computer Architecture and Parallel Processing. New York: McGraw-Hill, 1984.
[14] D. W. Jones, "Concurrent operations on priority queues,"Commun. ACM, vol. 32, pp. 132-137, 1989.
[15] C. J. H. McDiarmid and B. A. Reed, "Building heaps fast,"J. Algorithms, vol. 10, pp. 351-365, 1989.
[16] O. Nevalainen and J. Teuhola, "Priority queue administration by sublist index,"The Comput. J., vol. 22, pp. 220-224, 1977.
[17] S. Olariu and Z. Wen, "The mmp heap and its variations," Tech. Rep. TR-89-33, Dep. Comput. Sci., Old Dominion Univ., Sept. 1989.
[18] S. Olariu and Z. Wen, "Fast parallel heap algorithms," Tech. Rep. TR-90-12, Dep. Comput. Sci., Old Dominion Univ., Feb. 1990.
[19] M. C. Pinotti and G. Pucci, "Parallel priority queue," inProc. 28th Annu. Allerton Conf. Commun., Contr., Comput., 1990, to be published.
[20] M. Quinn,Designing Efficient Algorithms for Parallel Computers. New York: McGraw-Hill, 1987.
[21] M. J. Quinn and N. Deo, "Parallel graph algorithms,"ACM Comput. Surveys, vol. 16, pp. 319-348, Sept. 1984.
[22] V. N. Rao and V. Kumar, "Concurrent access of priority queues,"IEEE Trans. Comput.vol. 37, pp. 1657-1665, 1988.
[23] D. S. Richards and J. S. Salowe, "Stacks, queues, and dequeues with order-statistic operations," inProc. 28th Annu. Allerton Conf. Commun., Contr., Comput., 1990, to be published.
[24] U. Vishkin, "Synchronous parallel computation--A survey," TR 71, Dep. Comput. Sci., Courant Institute, N.Y.U., 1983.
[25] Y. B. Yoo, "Parallel processing for some network optimization problems," Ph.D. dissertation, Dep. Comput. Sci., Washington State Univ., Pullman, WA, 1983.

Index Terms:
Index Termsparallel initialization algorithms; adaptive parallel algorithm; priority queue structure;n-element array; parallel construction algorithms; heap-like structures; double-endedpriority queues; min-max heaps; deeps; min-max-pair heaps; processors;exclusive-read-exclusive-write parallel random-access machine; computationalcomplexity; data structures; parallel algorithms; queueing theory
S. Olariu, Z. Wen, "Optimal Parallel Initialization Algorithms for a Class of Priority Queues," IEEE Transactions on Parallel and Distributed Systems, vol. 2, no. 4, pp. 423-429, Oct. 1991, doi:10.1109/71.97899
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