All-to-All Personalized Communication in Multidimensional Torus and Mesh Networks

• Authors: Young-Joo Suh;Kang G. Shin
• Venue: IEEE Transactions on Parallel and Distributed Systems
• Year: 2001

All-to-all personalized communication commonly occurs in many important parallel algorithms, such as FFT and matrix transpose. This paper presents new algorithms for all-to-all personalized communication or complete exchange in multidimensional torus- or mesh-connected multiprocessors. For an $R \times C$ torus or mesh where $R \leq C$, the proposed algorithms have time complexities of $O(C)$ message startups and $O(RC^2)$ message transmissions. The algorithms for three- or higher-dimensional tori or meshes follow a similar structure. Unlike other existing message-combining algorithms in which the number of nodes in each dimension should be a power-of-two and square, the proposed algorithms accommodate non-power-of-two tori or meshes where the number of nodes in each dimension need not be power-of-two and square. 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 savings of message-rearrangement time.