Optimal Direct-Connect Topologies for Collective Communications

We consider the problem of distilling optimal network topologies for collective communications. We provide an algorithmic framework for constructing direct-connect topologies optimized for the latency-bandwidth tradeoff given a collective communication workload. Our algorithmic framework allows us to start from small base topologies and associated communication schedules and use a set of techniques that can be iteratively applied to derive much larger topologies and associated schedules. Our approach allows us to synthesize many different topologies and schedules for a given cluster size and degree constraint, and then identify the optimal topology for a given workload. We provide an analytical-model-based evaluation of the derived topologies and results on a small-scale optical testbed that uses patch panels for configuring a topology for the duration of an application's execution. We show that the derived topologies and schedules provide significant performance benefits over existing collective communications implementations.