Communication-Efficient Distributed Computing Through Combinatorial Multi-Access Models

Abstract: This paper explores the multi-access distributed computing (MADC) model, a novel distributed computing framework where mapper and reducer nodes are distinct entities. Unlike traditional MapReduce frameworks, MADC leverages coding-theoretic techniques to minimize communication overhead without necessitating file replication across mapper nodes. We introduce a new approach utilizing combinatorial designs, specifically t-designs, to construct efficient coding schemes that achieve a computation load of 1. By establishing a connection between t-designs and MapReduce Arrays, we characterize the achievable communication loads and demonstrate the flexibility of our method in selecting the number of reducer nodes. The proposed scheme significantly reduces the number of reducer nodes relative to existing combinatorial topology schemes, at the expense of increased communication cost.