Optimal all-to-all personalized exchange in 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. On the other hand, a mesh/torus has a constant node degree and better scalability, but the all-to-all personalized exchange algorithms have higher time complexity. The authors propose an alternative approach to efficient all-to-all personalized exchange by considering another important type of network, multistage networks for parallel computing systems. We present a new all-to-all personalized exchange algorithm for a class of unique-path 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×n network, which is optimal for all-to-all personalized exchange