Optimal parallel merging and sorting without memory conflicts
IEEE Transactions on Computers
Optimal computation of prefix sums on a binary tree of processors
International Journal of Parallel Programming
SIAM Journal on Computing
The design and analysis of parallel algorithms
The design and analysis of parallel algorithms
Efficient Parallel Binary Search on Sorted Arrays, with Applications
IEEE Transactions on Parallel and Distributed Systems
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Two arrays of numbers sorted in nondecreasing order are given: an array A of size n and an array B of size m, where nm. 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 nor=m/log m. It is shown how the solution obtained leads to an improved parallel merging algorithm.