Algorithms for Isotropic Tasks in Hypercubes and Wraparound

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. WVe 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. 1 Research supported by NSF under Grant NSF-ECS-8519058 and by the ARO under Grant DAAL03-b6K-0171. 2 Laboratory for Information and Decision Systems, M.I.T, Cambridge, Mass. 02139.