Multiple-multicast on FB-Clos network

Abstract

Multicast and multiple-multicast are important operations in parallel and distributed systems, and can be performed without blocking on a Clos network. However, the hardware cost of a non-blocking multicast and multiple-multicast Clos network is very high. The necessary and sufficient condition of a non-blocking multiple-multicast Clos network is that the number of middle-stage switches m satisfies m/spl ges//spl Theta/(n(log/r)/(log log r)), while there are r switches of n/spl times/m in the input stage. In a N/spl times/N Clos network the routing time complexity of the multicast algorithm is /spl Theta/(N) and that of multiple-multicast is /spl Theta/(N/sup 3/2/). We present an algorithm for multiple-multicast on a FB-Clos network which we proposed previously. The sufficient number of middle-stage switches for non-blocking multiple-multicast on a FB-Clos network decreases from m/spl ges//spl Theta/(n(log r)/(log log r)) to m/spl ges/3n+r-1. The routing time complexity of the algorithm for multiple-multicast decreases from /spl Theta/(N/sup 3/2/) to /spl Theta/(log/sup 2/ N log m). Both the hardware cost and routing time complexity are much lower than those of the Clos network.