We describe our work on improving the performance of collective communication operations in MPICH for clusters connected by switched networks. For each collective operation, we use multiple algorithms depending on the message size, with the goal of minimizing latency for short messages and minimizing bandwidth use for long messages. Although we have implemented new algorithms for all MPI (Message Passing Interface) collective operations, because of limited space we describe only the algorithms for allgather, broadcast, all-to-all, reduce-scatter, reduce, and allreduce. Performance results on a Myrinet-connected Linux cluster and an IBM SP indicate that, in all cases, the new algorithms significantly outperform the old algorithms used in MPICH on the Myrinet cluster, and, in many cases, they outperform the algorithms used in IBM's MPI on the SP. We also explore in further detail the optimization of two of the most commonly used collective operations, allreduce and reduce, particularly for long messages and nonpower-of-two numbers of processes. The optimized algorithms for these operations perform several times better than the native algorithms on a Myrinet cluster, IBM SP, and Cray T3E. Our results indicate that to achieve the best performance for a collective communication operation, one needs to use a number of different algorithms and select the right algorithm for a particular message size and number of processes.

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Abstract.A 5-year-profiling in production mode at the University of Stuttgart has shown that more than 40% of the execution time of Message Passing Interface (MPI) routines is spent in the collective communication routines MPI Allreduce and MPI Reduce. Although MPI implementations are now available for about 10 years and all vendors are committed to this Message Passing Interface standard, the vendors' and publicly available reduction algorithms could be accelerated with new algorithms by a factor between 3 (IBM, sum) and 100 (Cray T3E, maxloc) for long vectors. This paper presents five algorithms optimized for different choices of vector size and number of processes. The focus is on bandwidth dominated protocols for power-of-two and non-power-of-two number of processes, optimizing the load balance in communication and computation.

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