Distributed anonymous function computation in information fusion and multiagent systems

TL;DR

This paper introduces a model for distributed function computation in anonymous, resource-limited networks, characterizes computable functions, and explores approximation capabilities, with a focus on distributed averaging.

Contribution

It defines a new model for deterministic distributed computation with anonymous nodes and bounded resources, and characterizes the class of functions that can be computed or approximated.

Findings

Identifies a class of non-computable functions within the model

Proves that functions outside this class can be approximated

Highlights the importance of distributed averaging in the computation process

Abstract

We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes, with bounded computation and storage capabilities that do not scale with the network size. Our goal is to characterize the class of functions that can be computed within this model. In our main result, we exhibit a class of non-computable functions, and prove that every function outside this class can at least be approximated. The problem of computing averages in a distributed manner plays a central role in our development.