Optimal broadcast for fully connected processor-node networks

We develop and implement an optimal broadcast algorithm for fully connected processor networks under a bidirectional communication model in which each processor can simultaneously send a message to one processor and receive a message from another, possibly different processor. For any   number of processors pp the algorithm requires N−1+⌈logp⌉N−1+⌈logp⌉ communication rounds to broadcast NN blocks of data from a root processor to the remaining processors, meeting the lower bound in the model. For data of size mm, assuming that sending and receiving data of size m′m′ takes time α+βm′α+βm′, the best running time that can be achieved by the division of mm into equal-sized blocks is ((⌈logp⌉−1)α+βm)2. The algorithm uses a regular, circulant graph communication pattern, and degenerates into a binomial tree broadcast when the number of blocks to be broadcast is one. The algorithm is furthermore well suited to fully connected clusters of SMP (Symmetric Multi-Processor) nodes. The algorithm is implemented as part of an MPI (Message Passing Interface) library. We demonstrate significant practical bandwidth improvements of up to a factor 1.5 over several other, commonly used broadcast algorithms on both a small SMP cluster and a 72 node NEC SX vector supercomputer.