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Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case
"... Given an integer h, a graph G = (V, E) with arbitrary positive edge capacities and k pairs of vertices (s1, t1), (s2, t2),..., (sk, tk), called terminals, an hroute cut is a set F ⊆ E of edges such that after the removal of the edges in F no pair si−ti is connected by h edgedisjoint paths (i.e., t ..."
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Cited by 2 (1 self)
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that s1 = s2 = · · · = sk, called the single source case. As a corollary of it we obtain an approximate duality theorem for multiroute multicommodity flows and cuts with a single source. This partially answers an open question posted in several previous papers dealing with cuts for multicommodity
Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel BallGrowing
 THEORY OF COMPUTING SYSTEMS
, 2012
"... An elementary hroute flow, for an integer h ≥ 1, is a set of h edgedisjoint paths between a source and a sink, each path carrying a unit of flow, and an hroute flow is a nonnegative linear combination of elementary hroute flows. An hroute cut is a set of edges whose removal decreases the maxim ..."
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Cited by 3 (1 self)
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the maximum hroute flow between a given sourcesink pair (or between every sourcesink pair in the multicommodity setting) to zero. The main result of this paper is an approximate duality theorem for multicommodity hroute cuts and flows, for h ≤ 3: The size of a minimum hroute cut is at least f
Single Source Multiroute Flows and Cuts on Uniform Capacity Networks
, 2007
"... For an integer h ≥ 1, an elementary hroute flow is a flow along h edge disjoint paths between a source and a sink, each path carrying a unit of flow, and a single commodity hroute flow is a nonnegative linear combination of elementary hroute flows. An instance of a single source multicommodity f ..."
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Cited by 6 (2 self)
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flow problem for a graph G = (V, E) consists of a source vertex s ∈ V and k sinks t1,..., tk ∈ V; we denote it I = (s; t1,..., tk). In the single source multicommodity multiroute flow problem, we are given an instance I = (s; t1,..., tk) and an integer h ≥ 1, and the objective is to maximize the total
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
Fast Approximation Algorithms for Multicommodity Flow Problems
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1991
"... All previously known algorithms for solving the multicommodity flow problem with capacities are based on linear programming. The best of these algorithms [15] uses a fast matrix multiplication algorithm and takes O(k 3:5 n 3 m :5 log(nDU )) time for the multicommodity flow problem with inte ..."
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Cited by 191 (21 self)
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is needed to find an exact solution. As a consequence, even multicommodity flow problems with just a few commodities are believed to be much harder than singlecommodity maximumflow or minimumcost flow problems. In this paper, we describe the first polynomialtime combinatorial algorithms
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
ChernSimons Gauge Theory as a String Theory
, 2003
"... Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given spacetime interpretations. For instance, threedimensional ChernSimons gaug ..."
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Cited by 551 (14 self)
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Simons gauge theory can arise as a string theory. The worldsheet model in this case involves a topological sigma model. Instanton contributions to the sigma model give rise to Wilson line insertions in the spacetime ChernSimons theory. A certain holomorphic analog of ChernSimons theory can also arise as a
Wireless Communications
, 2005
"... Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University ..."
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Cited by 1129 (32 self)
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Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University
Results 1  10
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