On Parallel Integer Merging

The problem of merging two sorted arrays A = (a₁, a₂, ..., a_n1) and B = (b₁, b₂, ..., b_n2) is considered. For input elements that are drawn from a domain of integers 1...s] we present an algorithm that runs in O(log log log s) time using n/log log log s CREW PRAM processors (optimal speed-up) and O(ns^ε) space, where n = n₁ + n₂. For input elements that are drawn from a domain of integers 1...n] we present a second algorithm that runs in O(α(n)) time (where α(n) is the inverse of Ackermann′s function) using n/α(n) CREW PRAM processors and linear space. This second algorithm is non-uniform; however, it can be made uniform at a price of a certain loss of speed, or by using a CRCW PRAM.