Bandwidth-optimal all-to-all exchanges in fat tree networks

Abstract

The personalized all-to-all collective exchange is one of the most challenging communication patterns in HPC applications in terms of performance and scalability. In the context of the fat tree family of interconnection networks, widely used in current HPC systems and datacenters, we show that there is potential for optimizing this traffic pattern by deriving a tight theoretical lower bound for the bandwidth needed in the network to support such communication in a non-contending way. Current state of the art methods require up to twice as much bisection bandwidth as this theoretical minimum. We propose a set of optimized exchanges that use exactly the minimum amount of resources and exhibit close to ideal performance. This enables cost-effective networks, i.e., with as little as half the bisection bandwidth required by current state of the art methods, to exhibit quasi optimal performance under all-to-all traffic. In addition to supporting our claims by mathematical proofs, we include simulation results that confirm their correctness in practical system configurations. © 2013 ACM.