Generating cartesian products of two sets on a shuffle‐exchange network

Abstract

AbstractThis paper describes a method which generates all elements of a Cartesian product of two sets, using the shuffle‐exchange network. Often, processing appears which requires all elements of the Cartesian product in various fields in computer science as well as set manipulations in mathematics. Consequently, this operation can be considered to be one of the most fundamental. In this paper, the Cartesian product of two sets with N/2 elements is generated by an N‐input, N/2‐stage shuffle‐exchange network by assigning the switching element to each element of the Cartesian product. The experimental derivation of the realization method and the result of the experiment are described. In the derivation of the realization method, some properties of the shuffle‐exchange network are discussed. In the realization of the Cartesian product by an N/2‐stage shuffle‐exchange network, no redundant switching element is used. Consequently, the method shown in this paper is optimal.