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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
Engineering Multilevel Graph Partitioning Algorithms
"... We present a multilevel graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from multigrid linear solvers. Local improvement algorithms are based on maxflow mincut computations and more localized FM searches. By combining these technique ..."
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Cited by 28 (14 self)
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We present a multilevel graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from multigrid linear solvers. Local improvement algorithms are based on maxflow mincut computations and more localized FM searches. By combining
Reduced Communication Costs via Network Flow and Scheduling for Partitions of Dynamically Reconfigurable FPGAs *
"... This paper presents a dynamically reconfigurable FPGA partitioning algorithm for netlistlevel circuits. The proposed algorithm combines traditional maxflow mincut computing with a scheduling mechanism to improve maximum communication costs. Application of our previously published scheduling mecha ..."
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This paper presents a dynamically reconfigurable FPGA partitioning algorithm for netlistlevel circuits. The proposed algorithm combines traditional maxflow mincut computing with a scheduling mechanism to improve maximum communication costs. Application of our previously published scheduling
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.
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
Improved Bounds on the MaxFlow MinCut Ratio for Multicommodity Flows
, 1993
"... In this paper we consider the worst case ratio between the capacity of mincuts and the value of maxflow for multicommodity flow problems. We improve the best known bounds for the mincut maxflow ratio for multicommodity flows in undirected graphs, by replacing the O(log D) in the bound by O(log ..."
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Cited by 22 (2 self)
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In this paper we consider the worst case ratio between the capacity of mincuts and the value of maxflow for multicommodity flow problems. We improve the best known bounds for the mincut maxflow ratio for multicommodity flows in undirected graphs, by replacing the O(log D) in the bound by O
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
On the MaxFlow MinCut Ratio for Directed Multicommodity Flows
 Theor. Comput. Sci
, 2003
"... We give a pure combinatorial problem whose solution determines maxflow mincut ratio for directed multicommodity flows. In addition, this combinatorial problem has applications in improving the approximation factor of Greedy algorithm for maximum edge disjoint path problem. More precisely, our u ..."
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Cited by 7 (1 self)
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We give a pure combinatorial problem whose solution determines maxflow mincut ratio for directed multicommodity flows. In addition, this combinatorial problem has applications in improving the approximation factor of Greedy algorithm for maximum edge disjoint path problem. More precisely, our
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
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.
Results 1  10
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