Network coding for computing

Abstract

The following network computation problem is considered. A set of source nodes in an acyclic network generates independent messages and a single receiver node computes a function f of the messages. The objective is to characterize the maximum number of times f can be computed per network usage. The network coding problem for a single receiver network is a special case of the network computation problem (taking f to be the identity map) in which all of the source messages must be reproduced at the receiver. For network coding with a single receiver, routing is known to be rate-optimal and achieves the network min-cut upper bound. We give a generalized min-cut upper bound for the network computation problem. We show that the bound reduces to the usual network min-cut when f is the identity and the bound is tight for the computation of ldquodivisible functionsrdquo over ldquotree networksrdquo. We also show that the bound is not tight in general.