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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
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
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 11 (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.
A Topological MaxFlowMinCut Theorem
"... This note surveys a novel algebraictopological version of the maxflowmincut (MFMC) theorem for directed networks with capacity constraints. Novel features include the encoding of capacity constraints as a sheaf of semimodules over the network and a realization of flow and cut values as a direct ..."
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Cited by 2 (2 self)
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This note surveys a novel algebraictopological version of the maxflowmincut (MFMC) theorem for directed networks with capacity constraints. Novel features include the encoding of capacity constraints as a sheaf of semimodules over the network and a realization of flow and cut values as a
MaxFlow MinCut Theorems for MultiUser Communication Networks
, 2011
"... 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
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
A MaxFlow MinCut Theorem with Applications in Small Worlds and Dual Radio Networks
, 2009
"... Intrigued by the capacity of random networks, we start by proving a maxflow mincut theorem that is applicable to any random graph obeying a suitably defined independenceincut property. We then show that this property is satisfied by relevant classes, including small world topologies, which are p ..."
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Intrigued by the capacity of random networks, we start by proving a maxflow mincut theorem that is applicable to any random graph obeying a suitably defined independenceincut property. We then show that this property is satisfied by relevant classes, including small world topologies, which
An Approximate MaxFlow MinCut Theorem for Uniform Multicommodity Flow Problems with Applications to Approximation Algorithms
, 1989
"... In this paper, we consider a multicommodity flow problem where for each pair of vertices, (u,v), we are required to sendf halfunits of commodity (uv) from u to v and f halfunits of commodity (vu) from v to u without violating capacity constraints. Our main result is an algorithm for performing th9 ..."
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Cited by 246 (12 self)
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9 task provided that the capacity of each cut exceeds the demand across the cut by a b(log n) factor. The condition on cuts is required in the worst case, and is trivially within a i(log n) factor of optimal for any flow problem. The result is of interest because it can be used to construct
Bounds on the MaxFlow MinCut Ratio for Directed Multicommodity Flows
, 1993
"... The most wellknown theorem in combinatorial optimization is the classical maxflow mincut theorem of Ford and Fulkerson. This theorem serves as the basis for deriving efficient algorithms for finding maxflows and mincuts. Starting with the work of Leighton and Rao, significant effort was directe ..."
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Cited by 8 (3 self)
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The most wellknown theorem in combinatorial optimization is the classical maxflow mincut theorem of Ford and Fulkerson. This theorem serves as the basis for deriving efficient algorithms for finding maxflows and mincuts. Starting with the work of Leighton and Rao, significant effort
Results 1  10
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