All-to-all personalized exchange algorithms in generalized shuffle-exchange networks

All-to-all personalized exchange (ATAPE) occurs in many parallel applications. Previous ATAPE algorithms were mainly developed for hypercube, mesh, and torus networks. Recently, Yang and Wang [8] and also Massini [4] proposed an alternative approach to ATAPE by using multistage interconnection networks (MINs); they proposed new ATAPE algorithms for a class of unique-path, self-routable MINs (for example, baseline, shuffle-exchange (or omega), banyan network, and the reverse networks of these networks). However, the algorithms in [4] and [8] require that the given MIN must have unique-path property and satisfy N = 2ⁿ, in which N is the number of inputs (outputs) and n is the number of stages in the MIN. In [5], Padmanabhan proposed the generalized shuffle-exchange network (GSEN), which allows N to be any even number. Since the GSEN is not a unique-path MIN, the algorithms in [4] and [8] do not work on it. The purpose of this paper is to consider ATAPE in MINs without unique-path property. To our knowledge, no one has studied ATAPE in this type of MINs. We prove that under stage control technique, ATAPE algorithms for GSENs require at least 2ⁿ rounds. We propose an algorithm which uses a variation of stage control and works for all N ≡ 2 (mod 4). We will prove that our algorithm takes N rounds and therefore is optimal.