Revisiting the allocation of regular data arrays to a mesh of processors

The authors study the allocation of regular data arrays like images or matrices onto a network of processors. They investigate how to minimize the total communication time, while taking into account the time of constructing the messages. They show how to find the optimal mesh parameters as a function of problem-dependent and machine-dependent parameters. The main result is that, because of the reindexing time, the optimal mesh does not partition the data into square subdomains. It is also shown that the linear network (pipeline) very often performs better than a real 2-D mesh, since it avoids the reindexing of messages. They report numerical experiments performed on the TNode, a reconfigurable network of Transputers, and on the iPSC/860 hypercube, in which arbitrary grids can be embedded