Multi-Access Distributed Computing

Coded distributed computing (CDC) is a new technique proposed with the purpose of decreasing the intense data exchange required for parallelizing distributed computing systems. Under the famous MapReduce paradigm, this coded approach has been shown to decrease this communication overhead by a factor that is linearly proportional to the overall computation load during the mapping phase. In this paper, we propose multi-access distributed computing (MADC) as a generalization of the original CDC model, where now mappers (nodes in charge of the map functions) and reducers (nodes in charge of the reduce functions) are distinct computing nodes that are connected through a multi-access network topology. Focusing on the MADC setting with combinatorial topology, which implies
$\Lambda $
mappers and
$K$
reducers such that there is a unique reducer connected to any
$\alpha $
mappers, we propose a coded scheme and an information-theoretic converse, which jointly identify the optimal inter-reducer communication load, as a function of the computation load, to within a constant gap of 1.5. Additionally, a modified coded scheme and converse identify the optimal max-link communication load across all existing links to within a gap of 4.