Optimal All-to-All Personalized Exchange in Self-Routable Multistage Networks

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 O(n) time complexity for an n/spl times/n 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.