Parallel binary search

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 0(n log m, which is O(m)) for n &le m/log m. It is shown how the solution obtained here leads to an improved parallel merging algorithm.