Distributed Computing of Functions of Structured Sources with Helper Side Information

TL;DR

This paper introduces a new coding scheme for distributed function computation from correlated sources with helper side information, significantly reducing communication costs and computational complexity by exploiting source structure and function symmetry.

Contribution

It presents a novel achievable coding scheme tailored for general mixture models of sources, improving efficiency in distributed computing tasks.

Findings

Substantial reduction in communication costs.

Linear complexity in joint decoding.

Applicable to real-world scenarios like learning and graph neural networks.

Abstract

In this work, we consider the problem of distributed computing of functions of structured sources, focusing on the classical setting of two correlated sources and one user that seeks the outcome of the function while benefiting from low-rate side information provided by a helper node. Focusing on the case where the sources are jointly distributed according to a very general mixture model, we here provide an achievable coding scheme that manages to substantially reduce the communication cost of distributed computing by exploiting the nature of the joint distribution of the sources, the side information, as well as the symmetry enjoyed by the desired functions. Our scheme -- which can readily apply in a variety of real-life scenarios including learning, combinatorics, and graph neural network applications -- is here shown to provide substantial reductions in the communication costs, while simultaneously providing computational savings by reducing the exponential complexity of joint decoding techniques to a complexity that is merely linear.