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<p><b>Abstract</b>—All-to-all personalized exchange is one of the most dense collective communication patterns and occurs in many important applications in parallel computing. Previous all-to-all personalized exchange algorithms were mainly developed for hypercube and mesh/torus networks. Although the algorithms for a hypercube may achieve optimal time complexity, the network suffers from unbounded node degrees and thus has poor scalability in terms of I/O port limitation in a processor. On the other hand, a mesh/torus has a constant node degree and better scalability in this aspect, but the all-to-all personalized exchange algorithms have higher time complexity. In this paper, we propose an alternative approach to efficient all-to-all personalized exchange by considering another important type of networks, multistage networks, for parallel computing systems. We present a new all-to-all personalized exchange algorithm for a class of unique-path, self-routable multistage networks. We first develop a generic method for decomposing all-to-all personalized exchange patterns into some permutations which are realizable in these networks, and then present a new all-to-all personalized exchange algorithm based on this method. The newly proposed algorithm has <tmath>$O(n)$</tmath> time complexity for an <tmath>$n \times n$</tmath> network, which is optimal for all-to-all personalized exchange. By taking advantage of fast switch setting of self-routable switches and the property of a single input/output port per processor in a multistage network, we believe that a multistage network could be a better choice for implementing all-to-all personalized exchange due to its shorter communication latency and better scalability.</p>
Parallel computing, interprocessor communication, collective communication, all-to-all communication, all-to-all personalized exchange, routing, multistage interconnection networks, Latin Square, permutation.

Y. Yang and J. Wang, "Optimal All-to-All Personalized Exchange in Self-Routable Multistage Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 11, no. , pp. 261-274, 2000.
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