Optimal Multipass Self-Routing Algorithms for Packet-Switched Multistage Networks

The Clos(m, n) network [1] is a three-stage rearrangeable network capable ofrouting any permutation on N = mn elements. It was proven recently that the three-stage Clos(m, n) network is not self-routing except when the first (and the last) stage contains only two ( ~ x ~)-switches [3]. However, such a network contains O(N2 ) elementary switches which is close to that of a full crossbar network. This paper presents a new algorithm for self-routing arbitrary permutations on the three-stage Clos(m, n) network, for yn :S m :S n and n ;::: 8, m ;::: 8. The algorithm is based on combining radix-sorting with row-column sorting techniques on two-dimensional arrays. Self-routing is achieved through a fixed number of passes through the Clos network. Hence, the algorithm is suitable for packet-switching applications. The proposed control algorithm for routing on a Clos(m, n) network is optimal since it requires O(N) operations, where N = mn. Moreover, the algorithm is distributed, or self-routing, in the sense that each r x r switch can be set up based solely on the destination tags of the r packets it receives. The proposed algorithm also results in an optimal control algorithm for routing arbitrary permutations through other types of networks such as the Delta network.