Parallel multiple search

Two sequences of items sorted in increasing order are given: a sequence A of size n and a sequence B of size m. It is required to determine, for every item of A, the smallest item of B (if one exists) that is larger than it. In this paper, we present two algorithms for the problem. The first algorithm requires O(log m + log n) time using n processors on an EREW PRAM. On an EREW PRAM with p( p≤min{ m, n}) processors, the second algorithm runs in O(log n + n p time when m≤ n,or in O(log m + ( n p )log(2 m n )) time when m>n. The second algorithm is optimal.