2 - Networks for Sorting

Abstract

This chapter presents algorithms for sorting the sequence of distinct integers on a variety of sorting networks. These are special-purpose networks consisting of a number of processors interconnected in a way that directly implements a parallel sorting algorithm. The network implements one of the simplest sorting algorithms, and the position of each element of a sequence of distinct integers on a variety of sorting networks in the sorted sequence is determined by counting the number of elements smaller than it. The network can store two elements of the sequence in two local registers. It can compare the contents of A and B, and put the result of the comparison in a third local register RANK. Using the binary-tree connections, it can send the contents of any of its registers to another processor. It can add the contents of a register or a constant to the contents of RANK. In the algorithm, each row of processors is associated with one of the input elements.