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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Vydáno v:	IEEE transactions on information theory Ročník 57; číslo 2; s. 1015 - 1030
Hlavní autoři:	Appuswamy, R, Franceschetti, M, Karamchandani, N, Zeger, K
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.02.2011 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	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
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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 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.
AbstractList	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. 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 of the messages. The objective is to maximize the average number of times [Formula Omitted] 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.
Author	Zeger, K Appuswamy, R Franceschetti, M Karamchandani, N
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SubjectTerms	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
Title	Network Coding for Computing: Cut-Set Bounds
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