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555,709
A New Mincut Maxflow Ratio for Multicommodity Flows
, 2002
"... We present an improved bound on the mincut maxflow ratio for multicommodity ow problems with specified demands. To obtain the numerator of this ratio, capacity of a cut is scaled by the demand that has to cross the cut. In the denominator, the maximum concurrent flow value is used. Our new bound i ..."
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Cited by 15 (0 self)
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We present an improved bound on the mincut maxflow ratio for multicommodity ow problems with specified demands. To obtain the numerator of this ratio, capacity of a cut is scaled by the demand that has to cross the cut. In the denominator, the maximum concurrent flow value is used. Our new bound
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
Excluded Minors, Network Decomposition, and Multicommodity Flow
, 1993
"... In this paper we show that, given a graph and parameters ffi and r, we can find either a Kr;r minor or an edgecut of size O(mr=ffi) whose removal yields components of weak diameter O(r 2 ffi); i.e., every pair of nodes in such a component are at distance O(r 2 ffi) in the original graph. Usi ..."
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Cited by 132 (7 self)
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. Using this lemma, we improve the best known bounds for the mincut maxflow ratio for multicommodity flows in graphs with forbidden small minors. In general graphs, it was known that the ratio is O(log k) for the uniformdemand case (the case where there is a unitdemand commodity between every pair
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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was directed towards finding approximate analogs for the undirected multicommodity flow problem. In this paper we consider an approximate maxflow mincut theorem for directed graphs. We prove a polylogarithmic bound on the worst case ratio between the minimum multicut and the value of the maximum
Hard Metrics From Cayley Graphs Of Abelian Groups
, 2009
"... Hard metrics are the class of extremal metrics with respect to embedding into Euclidean spaces; they incur Ω(log n) multiplicative distortion, which is as large as it can possibly get for any metric space of size n. Besides being very interesting objects akin to expanders and good errorcorrecting ..."
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Cited by 2 (0 self)
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correcting codes, and having a rich structure, such metrics are important for obtaining lower bounds in combinatorial optimization, e. g., on the value of MinCut/MaxFlow ratio for multicommodity flows. For more than a decade, a single family of hard metrics was known (Linial, London, Rabinovich (Combinatorica 1995
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
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
An O(log k) approximate mincut maxflow theorem and approximation algorithm
 SIAM J. Comput
, 1998
"... Abstract. It is shown that the minimum cut ratio is within a factor of O(log k) of the maximum concurrent flow for kcommodity flow instances with arbitrary capacities and demands. This improves upon the previously bestknown bound of O(log 2 k) and is existentially tight, up to a constant factor. A ..."
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Cited by 139 (6 self)
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. An algorithm for finding a cut with ratio within a factor of O(log k) of the maximum concurrent flow, and thus of the optimal mincut ratio, is presented.
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
Approximation algorithms for multicommoditytype problems with guarantees independent of the graph size
 IN: PROCEEDINGS, IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS
, 2009
"... Linial, London and Rabani [3] proved that the mincut maxflow ratio for general maximum concurrent flow problems (when there are k commodities) is O(log k). Here we attempt to derive a more general theory of Steiner cut and flow problems, and we prove bounds that are polylogarithmic in k for a muc ..."
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Cited by 31 (4 self)
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Linial, London and Rabani [3] proved that the mincut maxflow ratio for general maximum concurrent flow problems (when there are k commodities) is O(log k). Here we attempt to derive a more general theory of Steiner cut and flow problems, and we prove bounds that are polylogarithmic in k for a
Results 1  10
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555,709