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136
Approximate MaxFlow Min(multi)cut Theorems and Their Applications
 SIAM Journal on Computing
, 1993
"... Consider the multicommodity flow problem in which the object is to maximize the sum of commodities routed. We prove the following approximate maxflow minmulticut theorem: min multicut O(logk) max flow min multicut; where k is the number of commodities. Our proof is constructive; it enables us ..."
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Cited by 160 (3 self)
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for the latter problem. 1 Introduction Much of flow theory, and the theory of cuts in graphs, is built around a single theorem  the celebrated maxflow mincut theorem of Ford and Fulkerson [FF], and Elias, Feinstein and Shannon [EFS]. The power of this theorem lies in that it relates two fundamental graph
Wireless Network Information Flow
, 710
"... Abstract — We present an achievable rate for general deterministic relay networks, with broadcasting at the transmitters and interference at the receivers. In particular we show that if the optimizing distribution for the informationtheoretic cutset bound is a product distribution, then we have a ..."
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Cited by 55 (15 self)
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complete characterization of the achievable rates for such networks. For linear deterministic finitefield models discussed in a companion paper [3], this is indeed the case, and we have a generalization of the celebrated maxflow mincut theorem for such a network. I.
Twounicast is hard
 in 2014 IEEE International Symposium on Information Theory (ISIT
"... AbstractConsider the kunicast network coding problem over an acyclic wireline network: Given a rate vector ktuple, determine whether the network of interest can support k unicast flows with those rates. It is well known that the oneunicast problem is easy and that it is solved by the celebrated ..."
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Cited by 2 (0 self)
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by the celebrated maxflow mincut theorem. The hardness of kunicast problems with small k has been an open problem. We show that the twounicast problem is as hard as any kunicast problem for k ≥ 3. Our result suggests that the difficulty of a network coding instance is related more to the magnitude of the rates
Wireless Network Information Flow: A Deterministic Approach
, 2009
"... In contrast to wireline networks, not much is known about the flow of information over wireless networks. The main barrier is the complexity of the signal interaction in wireless channels in addition to the noise in the channel. A widely accepted model is the the additive Gaussian channel model, and ..."
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Cited by 296 (42 self)
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or more destinations (all interested in the same information) and an arbitrary number of relay nodes. This result is a natural generalization of the celebrated maxflow mincut theorem for wireline networks. We then use the insights obtained from the analysis of the deterministic model to study
Network Flow Based Multiway Partitioning with Area and Pin Constraints
 Proc. of the ACM International Symposium on Physical Design
, 1998
"... Network flow is an excellent approach to finding mincuts because of the celebrated maxflow mincut theorem. However, for a long time, it was perceived as computationally expensive and deemed impractical for circuit partitioning. Only until recently, FBB [1,2] successfully applied network flow to tw ..."
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Cited by 4 (1 self)
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Network flow is an excellent approach to finding mincuts because of the celebrated maxflow mincut theorem. However, for a long time, it was perceived as computationally expensive and deemed impractical for circuit partitioning. Only until recently, FBB [1,2] successfully applied network flow
Multicommodity maxflow mincut theorems and their use in designing approximation algorithms
 J. ACM
, 1999
"... In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied by ..."
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Cited by 357 (6 self)
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In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied
Wireless Network Information Flow: A Deterministic Approach
, 2009
"... In contrast to wireline networks, not much is known about the flow of information over wireless networks. The main barrier is the complexity of the signal interaction in wireless channels in addition to the noise in the channel. A widely accepted model is the the additive Gaussian channel model, and ..."
Abstract
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or more destinations (all interested in the same information) and an arbitrary number of relay nodes. This result is a natural generalization of the celebrated maxflow mincut theorem for wireline networks. We then use the insights obtained from the analysis of the deterministic model to study
A combinatorial study of linear deterministic relay networks
, 2009
"... In the last few years the so called linear deterministic model of relay channels has gained popularity as a means of studying the ow of information over wireless communication networks, and this approach generalizes the model of wireline networks which is standard in network optimization. There is r ..."
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Cited by 7 (2 self)
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. There is recent work extending the celebrated maxflow/mincut theorem to the capacity of a unicast session over a linear deterministic relay network which is modeled by a layered directed graph. This result was first proved by a random coding scheme over large blocks of transmitted signals. We demonstrate
NETWORK FLOWS AND THE MAXFLOW MINCUT THEOREM
, 2009
"... The MaxFlow MinCut Theorem is an elementary theorem within the field of network flows, but it has some surprising implications in graph theory. We define network flows, prove the MaxFlow MinCut Theorem, and show that this theorem implies Menger’s and König’s Theorems. ..."
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The MaxFlow MinCut Theorem is an elementary theorem within the field of network flows, but it has some surprising implications in graph theory. We define network flows, prove the MaxFlow MinCut Theorem, and show that this theorem implies Menger’s and König’s Theorems.
The maxflow mincut theorem for countable networks
, 2007
"... We prove a strong version of the the MaxFlow MinCut theorem for countable networks, namely that in every such network there exist a flow and a cut that are “orthogonal” to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain infin ..."
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Cited by 5 (1 self)
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We prove a strong version of the the MaxFlow MinCut theorem for countable networks, namely that in every such network there exist a flow and a cut that are “orthogonal” to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain
Results 1  10
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136