Communication algorithms for isotropic tasks in hypercubes and wraparound meshes

We consider a broad class of communication tasks, which we call isotropic, in a hypercube and in a wraparound mesh of processors. These tasks are characterized by a type of symmetry with respect to origin node. We show that executing such tasks in a minimum number of steps is equivalent to a matrix decomposition problem. We use this property to obtain minimum completion time algorithms. For a special communication task, the total exchange problem, we find algorithms that are simultaneously optimal with respect to completion time, and average packet delay. We also prove that a particularly simple type of shortest path algorithm executes isotropic tasks in time which is optimal within a small bound.