Sparse collective operations for MPI

We discuss issues in designing sparse (nearest neighbor) collective operations for communication and reduction operations in small neighborhoods for the message passing interface (MPI). We propose three such operations, namely a sparse gather operation, a sparse all-to-all, and a sparse reduction operation in both regular and irregular (vector) variants. By two simple experiments we show a) that a collective handle for message scheduling and communication optimization is necessary for any such interface, b) that the possibly different amount of communication between neighbors need to be taken into account by the optimization, and c) illustrate the improvements that are possible by schedules that possess global information compared to implementations that can rely on only local information. We discuss different forms the interface and optimization handles could take. The paper is inspired by current discussion in the MPI Forum.