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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 56 (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.
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 161 (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: 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 298 (46 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
"... Abstract. 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 imp ..."
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Cited by 370 (6 self)
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Abstract. 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
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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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
"... Abstract. 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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Abstract. 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.
unknown title
"... In this lecture, we focus on the Maximum Flow problem, which is to send as much data as possible from a source to a destination through a network. This problem is polynomial time solvable, and is the most wellstudied problem in combinatorial optimization. First, we will show the problem formulation ..."
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formulation. Then, we will discuss a general algorithm using augmenting path, and some polynomial time implementations of this general algorithm to efficiently solve the problem. Also, we will prove the celebrated maxflow mincut theorem, which shows that the optimal value of the Maximum Flow problem
The maxflow mincut theorem for countable networks
 J. Combin. Theory (Series B
"... Abstract. 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 co ..."
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Cited by 6 (1 self)
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Abstract. 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
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