On Parallel Integer Merging

Abstract

The problem of merging two sorted arrays A = ( a 1 , a 2 , ..., a n 1 ) and B = ( b 1 , b 2 , ..., b n 2 ) 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 = n 1 + n 2 . 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.