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427
Right Type Departmental Bulletin Paper
"... The celebrated duality theorem called maxflow mincut theorem on a finite network due to Ford and Fulkerson [1] has been generalized to many directions. Among them, we shall be interested in Strang’s work [4]. Strang’s results were further generalized by Nozawa [3] in the continuous case. Strang ga ..."
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The celebrated duality theorem called maxflow mincut theorem on a finite network due to Ford and Fulkerson [1] has been generalized to many directions. Among them, we shall be interested in Strang’s work [4]. Strang’s results were further generalized by Nozawa [3] in the continuous case. Strang
Quasi Polymatroidal Flow Networks
, 1995
"... In this paper we give a flow model on directed multigraphs by introducing reflexions of generalized polymatroids at vertices as constraints for the flow conservation. This model has the essential features of the classical flow model, primarily the maxflow mincut theorem and the polynomial algor ..."
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In this paper we give a flow model on directed multigraphs by introducing reflexions of generalized polymatroids at vertices as constraints for the flow conservation. This model has the essential features of the classical flow model, primarily the maxflow mincut theorem and the polynomial
A MaxFlow/MinCut Algorithm for a Class of Wireless Networks
, 2010
"... The linear deterministic model of relay channels is a generalization of the traditional directed network model which has become popular in the study of the flow of information over wireless communication networks. The maxflow/mincut theorem of Ford and Fulkerson has recently been extended to this ..."
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Cited by 5 (2 self)
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The linear deterministic model of relay channels is a generalization of the traditional directed network model which has become popular in the study of the flow of information over wireless communication networks. The maxflow/mincut theorem of Ford and Fulkerson has recently been extended
AN APPROXIMATE MAXFLOW MINCUT RELATION FOR Undirected Multicommodity Flow, . . .
, 1995
"... In this paper, we prove the first approximate maxflow mincut theorem for undirected mult icommodity flow. We show that for a feasible flow to exist in a mult icommodity problem, it is sufficient hat every cut's capacity exceeds its demand by a factor of O(logClogD), where C is the sum of all ..."
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Cited by 7 (1 self)
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In this paper, we prove the first approximate maxflow mincut theorem for undirected mult icommodity flow. We show that for a feasible flow to exist in a mult icommodity problem, it is sufficient hat every cut's capacity exceeds its demand by a factor of O(logClogD), where C is the sum of all
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 160 (3 self)
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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 graph
A Note on MaxFlowMinCut and Homomorphic Equivalence in Matroids
, 1996
"... In this note we point out that the validity of the maxflowmincut theorem in a matroid port M is equivalent to the homomorphic equivalence of the dual port M to a circuit in the category of matroid ports and strong port maps. As a consequence, restricting to the category of matroids with the stron ..."
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Cited by 1 (0 self)
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In this note we point out that the validity of the maxflowmincut theorem in a matroid port M is equivalent to the homomorphic equivalence of the dual port M to a circuit in the category of matroid ports and strong port maps. As a consequence, restricting to the category of matroids
Singlesink multicommodity flow with side constraints
"... In recent years, several new models for network flows have been analyzed, inspired by emerging telecommunication technologies. These include models of resilient flow, motivated by the introduction of high capacity optical links, coloured flow, motivated by WavelengthDivisionMultiplexed optical net ..."
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Cited by 3 (0 self)
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networks, unsplittable flow motivated by SONET networks, and confluent flow motivated by nexthop routing in internet protocol (IP) networks. In each model, the introduction of new sideconstraints means that a maxflow mincut theorem does not necessarily hold, even in the setting where all demands
Wireless Network Information Flow
, 710
"... Abstract — We present an achievable rate for general deterministic relay networks, with broadcasting at the transmitters and interference at the receivers. In particular we show that if the optimizing distribution for the informationtheoretic cutset bound is a product distribution, then we have a ..."
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Cited by 55 (15 self)
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complete characterization of the achievable rates for such networks. For linear deterministic finitefield models discussed in a companion paper [3], this is indeed the case, and we have a generalization of the celebrated maxflow mincut theorem for such a network. I.
If time permits, McKean’s theorem could be explained. Source: 4.4 in [MP10] References
"... 2. Frostman’s lemma & Riesz capacity Frostman’s lemma: If A ⊆ R d is a closed set such that H α (A)> 0, then there exists a Borel probability measure µ supported on A and a constant C> 0 such that µ(D) ≤ CD  α for all Borel sets D. Proof uses a representation of compact subsets of R d b ..."
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by trees and the maxflow mincut theorem. Definition of Rieszαcapacity
Network information flow
 IEEE TRANS. INFORM. THEORY
, 2000
"... We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a pointtopoint communication network on which a number of information sources are to be mulitcast to certain sets of destinations. We assume that the information source ..."
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Cited by 1967 (24 self)
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coding rate region. Our result can be regarded as the Maxflow Mincut Theorem for network information flow. Contrary to one’s intuition, our work reveals that it is in general not optimal to regard the information to be multicast as a “fluid” which can simply be routed or replicated. Rather
Results 11  20
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427