### Network Coding for Computing: Cut-Set BoundsNetwork Coding for Computing: Cut-Set Bounds

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 Author Appuswamy, Rathinakumar ♦ Franceschetti, Massimo ♦ Karamchandani, Nikhil ♦ Zeger, Ken Source arXiv.org Content type Text File Format PDF Date of Submission 2009-12-15 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics Subject Keyword Computer Science - Information Theory ♦ cs ♦ math Abstract The following \textit{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 \textit{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 \textit{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 and for computing linear target functions in any network. We also study the bound's tightness for different classes of target functions. In particular, we give a lower bound on the computing capacity in terms of the Steiner tree packing number and a different bound for symmetric functions. We also show that for certain networks and target functions, the computing capacity can be less than an arbitrarily small fraction of the min-cut bound. Educational Use Research Learning Resource Type Article