Network Coding for Computing: Cut-Set Bounds

Abstract—The following network computing problem is considered. Source nodes in a directed acyclic network generate independent messages and a single receiver node computes a target function f of the messages. The objective is to maximize the average number of times f can be computed per network usage, i.e., the “computing capacity”. The network coding problem for a single-receiver network is a special case of the network computing problem in which all of the source messages must be reproduced at the receiver. For network coding with a single receiver, routing is known to achieve the capacity by achieving the network min-cut upper bound. We extend the definition of min-cut to the network computing problem and show that the min-cut is still an upper bound on the maximum achievable rate and is tight for computing (using coding) any target function in multi-edge tree networks. It is also tight for computing linear target functions in any network. We also study the bound’s tightne...

• Type: Journal
• Year: 2011
• Where: TIT
• Authors: Rathinakumar Appuswamy, Massimo Franceschetti, Nikhil Karamchandani, Kenneth Zeger
• Keywords: Network Computing Problem, Target Functions, TIT 2011, Upper Bound