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Replica symmetry of the minimum matching
, 2011
"... We establish the soundness of the replica symmetric ansatz introduced by M. Mézard and G. Parisi for the minimum matching problem in the pseudodimension d mean field model for d ≥ 1. The case d = 1 corresponds to the π 2 /6limit for the assignment problem proved by D. Aldous in 2001. We introduce ..."
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We establish the soundness of the replica symmetric ansatz introduced by M. Mézard and G. Parisi for the minimum matching problem in the pseudodimension d mean field model for d ≥ 1. The case d = 1 corresponds to the π 2 /6limit for the assignment problem proved by D. Aldous in 2001. We introduce a gametheoretical framework by which we establish the analogous limit also for d> 1. 1
6.1.2. Split TCP 4 6.2. Design and Performance Analysis of Wireless Networks 5
"... c t i v it y e p o r t 2008 Table of contents ..."
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6.1.1.5. Best SINRs in Macro Cellular Networks 5
"... c t i v it y e p o r t 2009 Table of contents 1. Team.................................................................................... 1 ..."
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c t i v it y e p o r t 2009 Table of contents 1. Team.................................................................................... 1
Belief Propagation  Perspectives
, 2010
"... When a pair of nuclearpowered Russsian submarines were reported patrolling off the eastern seabord of the United States over the last summer, Pentagon officials expresed wariness over the Kremlin’s motivations. At the same time, these officials emphasized their confidence in the US Navy’s tracking ..."
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When a pair of nuclearpowered Russsian submarines were reported patrolling off the eastern seabord of the United States over the last summer, Pentagon officials expresed wariness over the Kremlin’s motivations. At the same time, these officials emphasized their confidence in the US Navy’s tracking capabilities: “We’ve known where they were”, a senior Defense Department Official told the New York Times, “and we’re not concerned about our ability to track the subs”. While the official did not divulge the methods used by the Navy to track submarines, the Times added that such tracking “can be done from aircraft, ships, underwater sensors or other submarines”. But the article failed to mention perhaps the most important part of modern tracking technology – the algorithm that fuses different measurements at different times. Nearly every modern tracking system is based on the seminal work of Rudolf Kalman (1960) who developed the optimal fusion algorithm for linear dynamics under Gaussian noise. This algorithm, now known simply as the “Kalman Filter” is used in a
Messagepassing in stochastic processing networks
, 2011
"... Simple, distributed and iterative algorithms, popularly known as messagepassing, have become the architecture of choice for emerging infrastructure networks and the canonical behavioral model for natural networks. Therefore designing, as well as understanding, messagepassing algorithms has become i ..."
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Simple, distributed and iterative algorithms, popularly known as messagepassing, have become the architecture of choice for emerging infrastructure networks and the canonical behavioral model for natural networks. Therefore designing, as well as understanding, messagepassing algorithms has become important. The purpose of this survey is to describe the stateofart of messagepassing algorithms in the context of dynamic resource allocation in the presence of uncertainty, a problem that is central to operations research (OR) and management science (MS). Various directions for future research are described in this context as well as connections beyond OR and MS are explained. Through this survey, we hope to convey the opportunity presented to the OR and MS community to benefit from and contribute to the growing interdisciplinary area of messagepassing algorithms.
DOI: 10.7155/jgaa.00310 Smoothed Analysis of Belief Propagation for MinimumCost Flow and Matching
, 2013
"... Belief propagation (BP) is a messagepassing heuristic for statistical inference in graphical models such as Bayesian networks and Markov random fields. BP is used to compute marginal distributions or maximum likelihood assignments and has applications in many areas, including machine learning, im ..."
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Belief propagation (BP) is a messagepassing heuristic for statistical inference in graphical models such as Bayesian networks and Markov random fields. BP is used to compute marginal distributions or maximum likelihood assignments and has applications in many areas, including machine learning, image processing, and computer vision. However, the theoretical understanding of the performance of BP remains limited. Recently, BP has been applied to combinatorial optimization problems. It has been proved that BP can be used to compute maximumweight matchings and minimumcost flows for instances with a unique optimum. The number of iterations needed for this is pseudopolynomial and hence BP is not efficient in general. We study BP in the framework of smoothed analysis and prove that with high probability the number of iterations needed to compute maximumweight matchings and minimumcost flows is bounded by a polynomial if the weights/costs of the edges are randomly perturbed. To prove our upper bounds, we use an isolation lemma by Beier and Vöcking (SIAM Journal on Computing, 2006) for the matching problem and we generalize an isolation lemma by Gamarnik, Shah, and Wei (Operations Research, 2012) for the mincost flow problem. We also prove lower tail bounds for the number of iterations that BP needs to converge that almost match our upper bounds. Submitted:
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"... Solutions to recursive distributional equations for the meanfield TSP and ..."
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Solutions to recursive distributional equations for the meanfield TSP and
Belief propagation for minimum weight manytoone matchings in
"... the random complete graph ..."
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