Collective Algorithms for Multiported Torus Networks
Modern supercomputers with torus networks allow each node to simultaneously pass messages on all of its links. However, most collective algorithms are designed to only use one link at a time. In this work, we present novel multiported algorithms for the scatter, gather, all-gather, and reduce-scatter operations. Our algorithms can be combined to create multiported reduce, all-reduce, and broadcast algorithms. Several of these algorithms involve a new technique where we relax the MPI message-ordering constraints to achieve high performance and restore the correctordering using an additional stage of redundant communication.
 According to our models, on an n-dimensional torus, our algorithms should allow for nearly a 2n-fold improvement in communication performance compared to known, single-ported torus algorithms. In practice, we have achieved nearly 6x better performance on a 32k-node 3-dimensional torus.