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Parallel Binary Search
April 1990 (vol. 1 no. 2)
pp. 247-250

Two arrays of numbers sorted in nondecreasing order are given: an array A of size n and an array B of size m, where n>m. It is required to determine, for every element of A, the smallest element of B (if one exists) that is larger than or equal to it. It is shown how to solve this problem on the EREW PRAM (exclusive-read exclusive-write parallel random-access machine) in O(logm logn/log log m) time using n processors. The solution is then extended to the case in which fewer than n processors are available. This yields an EREW PRAM algorithm for the problem whose cost is O(n log m, which is O(m)) for n>or=m/log m. It is shown how the solution obtained leads to an improved parallel merging algorithm.

[1] Selim G. Akl,The Design and Analysis of Parallel Algorithms. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[2] S. G. Akl and N. Santoro, "Optimal parallel merging and sorting without memory conflicts,"IEEE Trans. Comput., vol. C-36, pp. 1367-1369, 1987.
[3] R. Cole, "Parallel merge sort,"SIAM J. Comput., vol. 17, pp. 770-785, 1988.
[4] C. P. Kruskal, "Searching, merging, and sorting in parallel computation,"IEEE Trans. Comput., vol. C-32, pp. 942-946, Oct. 1983.
[5] S. D. Lang and N. Deo, "Recursive batched binary searching of sequential files,"The Comput. Journal, to be published.
[6] H. Meijer and S. G. Akl, "Optimal computation of prelix sums on a binary tree of processors,"Int. J. Parallel Programm., vol. 16, no. 2, pp. 127-136, Apr. 1987.
[7] H. Meijer and S. G. Akl, "Parallel binary search with delayed read conflicts," Tech. Rep. 89-257. Dep. Comput. Inform. Sci., Queen's University, Kingston, Ont., Canada, June 1989.

Index Terms:
Index Termsbinary search; cost optimality; nondecreasing order; EREW PRAM; parallel random-access machine; parallel merging algorithm; computational complexity; parallel algorithms; search problems
Citation:
S.G. Akl, H. Meijer, "Parallel Binary Search," IEEE Transactions on Parallel and Distributed Systems, vol. 1, no. 2, pp. 247-250, April 1990, doi:10.1109/71.80139
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