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Isomorphic (sparse) collective communication is a form of collectivecommunication in which all involved processes communicate in small, identicallystructured neighborhoods of other processes. Isomorphic neighborhoods aredefined via an embedding of the processes in a regularly structured topology,e.g., $d$-dimensional torus, which may correspond to the physical communicationnetwork of the underlying system. Isomorphic collective communication is usefulfor implementing stencil and other regular, sparse distributed computations,where the assumption that all processes behave (almost) symmetrically isjustified.  In this paper, we show how efficient message-combining communicationschedules for isomorphic, sparse collective communication can easily andefficiently be computed by purely local computations. We give schemes for\emph{isomorphic \alltoall} and \emph{\allgather} communication that reduce thenumber of communication rounds and thereby the communication latency from $s$to at most $Nd$, for neighborhoods consisting of $s$ processes with the (small)factor $N$ depending on the structure of the neighborhood and the capabilitiesof the communication system. Using these schedules, we give \emph{zero-copyimplementations} of the isomorphic collectives using MPI and its deriveddatatypes to eliminate explicit, process-local copy operations. By benchmarkingthe collective communication algorithms against straightforward implementationsand against the corresponding MPI neighborhood collectives, we documentsignificant latency improvements of our implementations for block sizes of upto a few kilobytes. We discuss further optimizations for computing even betterschedules, some of which have been implemented and benchmarked.

Message-Combining Algorithms for Isomorphic, Sparse Collective Communication