# All-to-All Personalized Exchange Algorithms in Generalized Shuffle-Exchange Networks

• Published 2009 in 2009 Eighth International Conference on Networks

#### Abstract

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\cite{YW3} and also Massini \cite{M} 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 \cite{M} and\cite{YW3} require that the given MIN must have unique-path property and satisfy $N=2^n$, in which $N$ is the number of inputs (outputs)and $n$ is the number of stages in the MIN. In \cite{P}, 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 \cite{M} and \cite{YW3} 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 TAPE in this type of MINs. We prove that under stage control technique, ATAPE algorithms for GSENs require at least $2^n$ rounds. We propose an algorithm which uses a variation of stage control and works for all $N \equiv 2 \pmod{4}$. We will prove that our algorithm takes $N$ rounds and therefore is optimal.

DOI: 10.1109/ICN.2009.58

### Cite this paper

@article{Chou2009AlltoAllPE, title={All-to-All Personalized Exchange Algorithms in Generalized Shuffle-Exchange Networks}, author={Well Y. Chou and Richard B. Chen and Chiuyuan Chen}, journal={2009 Eighth International Conference on Networks}, year={2009}, pages={185-190} }