Parallel merging with restriction

Abstract

In this paper, we study the merging of two sorted arrays $A=(a_{1},a_{2},\ldots, a_{n_{1}})$ and $B=(b_{1},b_{2},\ldots,b_{n_{2}})$ on EREW PRAM with two restrictions: (1) The elements of two arrays are taken from the integer range [1,n], where n=Max(n 1,n 2). (2) The elements are taken from either uniform distribution or non-uniform distribution such that $\#\{a\in A\,\mbox{and}\,b\in B\,\mbox{s.t.}\,a,b\in [(i-1)\frac{n}{p}+1,i\,\frac{n}{p}]\}=O(\frac{n}{p})$ , for 1?i?p?(number of processors). We give a new optimal deterministic algorithm runs in $O(\frac{n}{p})$ time using p processors on EREW PRAM. For $p=\frac{n}{\log^{(g)}{n}}$ ; the running time of the algorithm is O(log?(g) n) which is faster than the previous results, where log?(g) n=log?log?(g?1) n for g>1 and log?(1) n=log?n. We also extend the domain of input data to [1,n k ], where k is a constant.