Multicast on Irregular Switch-based Networks with Wormhole Routing 1

This paper presents eecient multicasting with reduced contention on irregular networks with switch-based wormhole interconnection and unicast message passing. First, it is proved that for an arbitrary irregular network with a typical deadlock-free, adaptive routing, it may not be possible to create an ordered list of nodes to implement an arbitrary multicast in a contention-free manner with minimal number of communication steps. Next, three diierent multicast algorithms are proposed with their respective node orderings to reduce contention: switch-based ordering (SO), switch-based hierarchical ordering (SHO), and chain concatenation ordering (CCO). A variation of a binomial tree-based communication pattern with unicast message passing is used on the above ordered lists to implement multicast. The proposed multicast algorithms are compared with each other as well as with the naive random ordering (RO) algorithm for a range of system sizes, switch sizes, message lengths, degrees of connectivity, destination set sizes, and communication start-up times. With larger system size and larger destination set size, the CCO algorithm is shown to be the best to implement multicast with reduced contention and minimum latency. The SHO algorithm emerges as the second best. Such results related to multicast on irregular networks are the rst of their kind in the wormhole literature. Thus, these results demonstrate signiicant potential to be applied to current and future generation NOW systems with irregular interconnection.