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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.

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Index Terms:
Index Termsbinary search; cost optimality; nondecreasing order; EREW PRAM; parallel random-access machine; parallel merging algorithm; computational complexity; parallel algorithms; search problems
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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