An all-to-all communication algorithm is said to be optimal if it has the smallest communication delay. Previous all-to-all personalized exchange algorithms are mainly for hypercube, mesh, and torus. In Yang and Wang (2000) , Yang and Wang proved that a multistage interconnection network (MIN) is a better choice for implementing all-to-all personalized exchange and they proposed optimal all-to-all personalized exchange algorithms for MINs. In Massini (2003) , Massini proposed a new optimal algorithm for MINs, which is independent of the network topology. Do notice that the algorithms in  and  work only for MINs with the unique path property (meaning that there is a unique path between each pair of source and destination) and satisfying N = 2n, in which N is the number of processors, 2 means all the switches are of size 2×2, and n is the number of stages. In Padmanabhan (1991) , Padmanabhan proposed the generalized shuffle-exchange network (GSEN), which is a generalization of the shuffle-exchange network. Since a GSEN does not have the unique path property, the algorithms in  and  cannot be used. The purpose of this paper is to consider the all-to-all personalized exchange problem in GSENs. An optimal algorithm and several bounds will be proposed.
- All-to-all communication
- All-to-all personalized exchange
- Multistage interconnection networks
- Omega network
- Parallel and distributed computing
- Shuffle-exchange networks