Summary: 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 \(p\) the algorithm requires \(N - 1+\lceil \log p\rceil\) communication rounds to broadcast \(N\) blocks of data from a root processor to the remaining processors, meeting the lower bound in the model. For data of size \(m\), assuming that sending and receiving data of size \(m^{\prime}\) takes time \(\alpha +\beta m^{\prime}\), the best running time that can be achieved by the division of \(m\) into equal-sized blocks is \(\sqrt{(\lceil \log p\rceil -1)\alpha} + \sqrt{\beta m})^2\). 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.