An Optimal Parallel Algorithm for Merging Using Multiselection

We consider the problem of merging two sorted arrays and on an exclusive read, exclusive write parallel random access machine (EREW PRAM, see [8] for a definition). Our approach consists of identifying elements in and which would have appropriate rank in the merged array. These elements partition the arrays and into equal-size subproblems which then can be assigned to each processor for sequential merging. Here, we present a novel parallel algorithm for selecting the required elements, which leads to a simple and optimal algorithm for merging in parallel. Thus, our technique differs from those of other optimal parallel algorithms for merging where the subarrays are defined by elements at fixed positions in and . Formally, the problem of selection can be stated as follows. Given two ordered multisets and of sizes and , where , the problem is to select the th smallest element in and combined. The problem can be solved sequentially in log time without explicitly merging and [5, 6]. Multiselection, a generalization of selection, is the problem where given a sequence of integers 1