Network Flows for Functions

TL;DR

This paper develops methods for in-network computation of arbitrary functions over capacity-constrained networks, optimizing data flow to maximize computation rate through linear programming and combinatorial algorithms.

Contribution

It introduces a framework for computing arbitrary functions in networks, formulating linear programs and designing algorithms for efficient in-network computation.

Findings

Linear programs effectively determine optimal network flows for function computation.

A fast combinatorial primal-dual algorithm provides approximate solutions efficiently.

Extensions include multiple terminals, multiple functions, and energy constraints.

Abstract

We consider in-network computation of an arbitrary function over an arbitrary communication network. A network with capacity constraints on the links is given. Some nodes in the network generate data, e.g., like sensor nodes in a sensor network. An arbitrary function of this distributed data is to be obtained at a terminal node. The structure of the function is described by a given computation schema, which in turn is represented by a directed tree. We design computing and communicating schemes to obtain the function at the terminal at the maximum rate. For this, we formulate linear programs to determine network flows that maximize the computation rate. We then develop fast combinatorial primal-dual algorithm to obtain $\epsilon$-approximate solutions to these linear programs. We then briefly describe extensions of our techniques to the cases of multiple terminals wanting different functions, multiple computation schemas for a function, computation with a given desired precision, and to networks with energy constraints at nodes.