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304,041
Polynomial time algorithms for multicast network code construction
 IEEE TRANS. ON INFO. THY
, 2005
"... The famous maxflow mincut theorem states that a source node can send information through a network ( ) to a sink node at a rate determined by the mincut separating and. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediat ..."
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Cited by 317 (31 self)
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The famous maxflow mincut theorem states that a source node can send information through a network ( ) to a sink node at a rate determined by the mincut separating and. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided
Polynomial Time Algorithms for Network Information Flow
 in 15th ACM Symposium on Parallel Algorithms and Architectures
, 2003
"... The famous maxflow mincut theorem states that a source node s can send information through a network (V; E) to a sink node t at a data rate determined by the mincut separating s and t. Recently it has been shown that this rate can also be achieved for multicasting to several sinks provided that t ..."
Abstract

Cited by 118 (1 self)
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The famous maxflow mincut theorem states that a source node s can send information through a network (V; E) to a sink node t at a data rate determined by the mincut separating s and t. Recently it has been shown that this rate can also be achieved for multicasting to several sinks provided
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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implied by the mincut. The result (which is existentially optimal) establishes an important analogue of the famous 1commodity maxflow mincut theorem for problems with multiple commodities. The result also has substantial applications to the field of approximation algorithms. For example, we use
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.
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
An Experimental Comparison of MinCut/MaxFlow Algorithms for Energy Minimization in Vision
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2001
"... After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in lowlevel vision. The combinatorial optimization literature provides many mincut/maxflow algorithms with different polynomial time compl ..."
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Cited by 1311 (54 self)
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After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in lowlevel vision. The combinatorial optimization literature provides many mincut/maxflow algorithms with different polynomial time
EHRHART CLUTTERS: REGULARITY AND MAXFLOW MINCUT
, 2010
"... If C is a clutter with n vertices and q edges whose clutter matrix has column vectors A = {v1,...,vq}, we call C an Ehrhart clutter if {(v1,1),...,(vq,1)} ⊂ {0,1} n+1 is a Hilbert basis. Letting A(P) be the Ehrhart ring of P = conv(A), we are able to show that if C is a uniform unmixed MFMC clutter ..."
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Cited by 4 (1 self)
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If C is a clutter with n vertices and q edges whose clutter matrix has column vectors A = {v1,...,vq}, we call C an Ehrhart clutter if {(v1,1),...,(vq,1)} ⊂ {0,1} n+1 is a Hilbert basis. Letting A(P) be the Ehrhart ring of P = conv(A), we are able to show that if C is a uniform unmixed MFMC clutter, then C is an Ehrhart clutter and in this case we provide sharp upper bounds on the CastelnuovoMumford regularity and the ainvariant of A(P). Motivated by the ConfortiCornuéjols conjecture on packing problems, we conjecture that if C is both ideal and the clique clutter of a perfect graph, then C has the MFMC property. We prove this conjecture for Meyniel graphs by showing that the clique clutters of Meyniel graphs are Ehrhart clutters. In much the same spirit, we provide a simple proof of our conjecture when C is a uniform clique clutter of a perfect graph. We close with a generalization of Ehrhart clutters as it relates to total dual integrality.
Approximate MaxFlow MinCut Theorems (Course Notes Extension for COMP5703)
, 2014
"... In this report, we discuss two approximate maxflow mincut theorems that first introduced by Tom Leighton and Satish Rao in 1988 [9] and extended in 1999 [10] for uniform multicommodity flow problems. In the theorems they first showed that for any nnode multicommodity flow problem with uniform de ..."
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In this report, we discuss two approximate maxflow mincut theorems that first introduced by Tom Leighton and Satish Rao in 1988 [9] and extended in 1999 [10] for uniform multicommodity flow problems. In the theorems they first showed that for any nnode multicommodity flow problem with uniform
The first eigenvalue of the Laplacian, isoperimetric constants, and the maxflow mincut theorem
, 2008
"... We show how ’test’ vector fields may be used to give lower bounds for the Cheeger constant of a Euclidean domain (or Riemannian manifold with boundary), and hence for the lowest eigenvalue of the Dirichlet Laplacian on the domain. Also, we show that a continuous version of the classical Max Flow Min ..."
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Cited by 10 (0 self)
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Min Cut Theorem for networks implies that Cheeger’s constant may be obtained precisely from such vector fields. Finally, we apply these ideas to reprove a known lower bound for Cheeger’s constant in terms of the inradius of a plane domain.
1MaxFlow MinCut Theorems for MultiUser Communication Networks
"... Traditionally, communication networks are modeled and analyzed in terms of information flows in graphs. In this paper, we introduce a novel symbolic approach to communication networks, where the topology of the underlying network is contained in a set of formal terms from logic. In order to account ..."
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problems in this setup. For a large class of measures containing the dispersion, we first show that the maximum flow of information transmitted to the users is asymptotically equal to the mincut of the term set, which represents the number of degrees of freedom of that term set. On the other hand
Results 1  10
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304,041