Wireless MapReduce Arrays for Coded Distributed Computing

TL;DR

This paper introduces wireless MapReduce arrays that enable efficient coded distributed computing over wireless channels, reducing the required number of files while maintaining optimal performance.

Contribution

It proposes a new scheme using wireless MapReduce arrays that significantly lowers the file number requirement compared to existing methods.

Findings

Achieves optimal performance with fewer files (order of number of nodes).

Designs a structured array representation for all three phases.

Connects wireless MapReduce arrays with multi-antenna coded caching schemes.

Abstract

We consider a wireless distributed computing system based on the MapReduce framework, which consists of three phases: \textit{Map}, \textit{Shuffle}, and \textit{Reduce}. The system consists of a set of distributed nodes assigned to compute arbitrary output functions depending on a file library. The computation of the output functions is decomposed into Map and Reduce functions, and the Shuffle phase, which involves the data exchange, links the two. In our model, the Shuffle phase communication happens over a full-duplex wireless interference channel. For this setting, a coded wireless MapReduce distributed computing scheme exists in the literature, achieving optimal performance under one-shot linear schemes. However, the scheme requires the number of input files to be very large, growing exponentially with the number of nodes. We present schemes that require the number of files to be in the order of the number of nodes and achieve the same performance as the existing scheme. The schemes are obtained by designing a structure called wireless MapReduce array that succinctly represents all three phases in a single array. The wireless MapReduce arrays can also be obtained from the extended placement delivery arrays known for multi-antenna coded caching schemes.