Efficient all-to-all personalized exchange in multidimensional torus networks

This paper presents new algorithms for all-to-all personalized exchange in multidimensional torus-connected multiprocessors. Unlike existing message-combining algorithms in which the number of nodes in each dimension should be power-of-two and square, the proposed algorithms accommodate non-power-of-two tori where the number of nodes in each dimension need not be power-of-two. In addition, destinations remain fixed over a larger number of steps in the proposed algorithms, thus making them amenable to optimizations. Finally, the data structures used are simple, hence making substantial saving of message-rearrangement time.