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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 146 (3 self)
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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 to find a multicut within O(log k) of the max flow (and hence also the optimal multicut). In addition, the proof technique provides a unified framework in which one can also analyse the case of flows with specified demands, of LeightonRao and Klein et.al., and thereby obtain an improved bound 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 graphtheoretic entities via the potent mechanism of a minmax relation. The importance of this theor...
Low Complexity Algebraic Multicast Network Codes
 IN IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT
, 2003
"... We present a low complexity algorithm for designing algebraic codes that achieve the information theoretic capacity for the multicast problem on directed acyclic networks. The properties ..."
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Cited by 24 (5 self)
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We present a low complexity algorithm for designing algebraic codes that achieve the information theoretic capacity for the multicast problem on directed acyclic networks. The properties
New DistanceDirected Algorithms for Maximum Flow and Parametric Maximum Flow Problems
, 1987
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AllPairs MinCut in Sparse Networks
, 1996
"... Algorithms are presented for the allpairs mincut problem in bounded treewidth, planar and sparse networks. The approach used is to preprocess the input nvertex network so that, afterwards, the value of a mincut between any two vertices can be efficiently computed. A tradeoff is shown between th ..."
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Cited by 5 (1 self)
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Algorithms are presented for the allpairs mincut problem in bounded treewidth, planar and sparse networks. The approach used is to preprocess the input nvertex network so that, afterwards, the value of a mincut between any two vertices can be efficiently computed. A tradeoff is shown between the preprocessing time and the time taken to compute mincuts subsequently. In particular, after an O(n log n) preprocessing of a bounded treewidth network, it is possible to find the value of a mincut between any two vertices in constant time. This implies that for such networks the allpairs mincut problem can be solved in time O(n 2 ). This algorithm is used in conjunction with a graph decomposition technique of Frederickson to obtain algorithms for sparse and planar networks. The running times depend upon a topological property, fl, of the input network. The parameter fl varies between 1 and \Theta(n); the algorithms perform well when fl = o(n). The value of a mincut can be found in t...