Fundamental Limits of Distributed Data Shuffling

Data shuffling of training data among different computing nodes (workers) has been identified as a core element to improve the statistical performance of modern large scale machine learning algorithms. Data shuffling is often considered one of the most significant bottlenecks in such systems due to the heavy communication load. Under a master-worker architecture (where a master has access to the entire dataset and only communications between the master and workers is allowed) coding has been recently proved to considerably reduce the communication load. This work considers a different communication paradigm referred to as distributed data shuffling, where workers, connected by a shared link, are allowed to communicate with one another while no communication between the master and workers is allowed. Under the constraint of uncoded cache placement, first a general coded distributed data shuffling scheme is proposed, which achieves the optimal communication load within a factor two; then, an improved scheme achieving the exact optimality for either large memory size or at most four workers in the system.