  Good process-to-compute-node mappings can be decisive for well performing HPC
applications. A special, important class of process-to-node mapping problems is
the problem of mapping processes that communicate in a sparse stencil pattern
to Cartesian grids. By thoroughly exploiting the inherently present structure
in this type of problem, we devise three novel distributed algorithms that are
able to handle arbitrary stencil communication patterns effectively. We analyze
the expected performance of our algorithms based on an abstract model of inter-
and intra-node communication. An extensive experimental evaluation on several
HPC machines shows that our algorithms are up to two orders of magnitude faster
in running time than a (sequential) high-quality general graph mapping tool,
while obtaining similar results in communication performance. Furthermore, our
algorithms also achieve significantly better mapping quality compared to
previous state-of-the-art Cartesian grid mapping algorithms. This results in up
to a threefold performance improvement of an MPI_Neighbor_alltoall exchange
operation. Our new algorithms can be used to implement the MPI_Cart_create
functionality.
