Network Coding for Computing: Cut-Set Bounds

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.,...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 57; no. 2; pp. 1015 - 1030
Main Authors: Appuswamy, R, Franceschetti, M, Karamchandani, N, Zeger, K
Format: Journal Article
Language:English
Published: New York IEEE 01.02.2011
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Capacity
Coding
Computation
Computational modeling
cut-set bound
Encoding
function computation
Indexes
information theory
Mathematical analysis
Mathematical models
Messages
Network coding
Networks
Receivers
Steiner trees
Studies
throughput
Upper bound
Upper bounds
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary: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 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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2010.2095070