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<p><b>Abstract</b>—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 <tmath>$R \times C$</tmath> torus or mesh where <tmath>$R \leq C$</tmath>, the proposed algorithms have time complexities of <tmath>$O(C)$</tmath> message startups and <tmath>$O(RC^2)$</tmath> 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.</p>
Collective communication, all-to-all personalized communication, complete exchange, direct exchange, message-combining, interprocessor communication.

K. G. Shin and Y. Suh, "All-to-All Personalized Communication in Multidimensional Torus and Mesh Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 12, no. , pp. 38-59, 2001.
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