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22,136
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
 In Proceedings of the 37th IEEE Symposium on Foundations of Computer Science (FOCS’96
, 1996
"... Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes a ..."
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Cited by 399 (3 self)
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to Christofides) achieves a 3/2approximation in polynomial time. We also give similar approximation schemes for some other NPhard Euclidean problems: Minimum Steiner Tree, kTSP, and kMST. (The running times of the algorithm for kTSP and kMST involve an additional multiplicative factor k.) The previous best
On the Construction of EnergyEfficient Broadcast and Multicast Trees in Wireless Networks
, 2000
"... wieselthier @ itd.nrl.navy.mil nguyen @ itd.nrl.navy.mil ..."
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Cited by 554 (13 self)
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wieselthier @ itd.nrl.navy.mil nguyen @ itd.nrl.navy.mil
Distributed hierarchical processing in the primate cerebral cortex
 Cereb Cortex
, 1991
"... In recent years, many new cortical areas have been identified in the macaque monkey. The number of identified connections between areas has increased even more dramatically. We report here on (1) a summary of the layout of cortical areas associated with vision and with other modalities, (2) a comput ..."
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Cited by 901 (6 self)
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In recent years, many new cortical areas have been identified in the macaque monkey. The number of identified connections between areas has increased even more dramatically. We report here on (1) a summary of the layout of cortical areas associated with vision and with other modalities, (2) a computerized database for storing and representing large amounts of information on connectivity patterns, and (3) the application of these data to the analysis of hierarchical organization of the cerebral cortex. Our analysis concentrates on the visual system, which includes 25 neocortical areas that are predominantly or exclusively visual in function, plus an additional 7 areas that we regard as visualassociation areas on the basis of their extensive visual inputs. A total of 305 connections among these 32 visual and
Predicting How People Play Games: Reinforcement Learning . . .
 AMERICAN ECONOMIC REVIEW
, 1998
"... ..."
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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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 fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can 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.
Logical foundations of objectoriented and framebased languages
 JOURNAL OF THE ACM
, 1995
"... We propose a novel formalism, called Frame Logic (abbr., Flogic), that accounts in a clean and declarative fashion for most of the structural aspects of objectoriented and framebased languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, ..."
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Cited by 880 (64 self)
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We propose a novel formalism, called Frame Logic (abbr., Flogic), that accounts in a clean and declarative fashion for most of the structural aspects of objectoriented and framebased languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, encapsulation, and others. In a sense, Flogic stands in the same relationship to the objectoriented paradigm as classical predicate calculus stands to relational programming. Flogic has a modeltheoretic semantics and a sound and complete resolutionbased proof theory. A small number of fundamental concepts that come from objectoriented programming have direct representation in Flogic; other, secondary aspects of this paradigm are easily modeled as well. The paper also discusses semantic issues pertaining to programming with a deductive objectoriented language based on a subset of Flogic.
Convergent Treereweighted Message Passing for Energy Minimization
 ACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI), 2006. ABSTRACTACCEPTED TO IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (PAMI)
, 2006
"... Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper we focus on the recent technique proposed by Wainwright et al. [33] treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy ..."
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Cited by 491 (16 self)
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Algorithms for discrete energy minimization are of fundamental importance in computer vision. In this paper we focus on the recent technique proposed by Wainwright et al. [33] treereweighted maxproduct message passing (TRW). It was inspired by the problem of maximizing a lower bound on the energy. However, the algorithm is not guaranteed to increase this bound it may actually go down. In addition, TRW does not always converge. We develop a modification of this algorithm which we call sequential treereweighted message passing. Its main property is that the bound is guaranteed not to decrease. We also give a weak tree agreement condition which characterizes local maxima of the bound with respect to TRW algorithms. We prove that our algorithm has a limit point that achieves weak tree agreement. Finally, we show that our algorithm requires half as much memory as traditional message passing approaches. Experimental results demonstrate that on certain synthetic and real problems our algorithm outperforms both the ordinary belief propagation and treereweighted algorithm in [33]. In addition, on stereo problems with Potts interactions we obtain a lower energy than graph cuts.
ROCK: A Robust Clustering Algorithm for Categorical Attributes
 In Proc.ofthe15thInt.Conf.onDataEngineering
, 2000
"... Clustering, in data mining, is useful to discover distribution patterns in the underlying data. Clustering algorithms usually employ a distance metric based (e.g., euclidean) similarity measure in order to partition the database such that data points in the same partition are more similar than point ..."
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Cited by 430 (2 self)
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Clustering, in data mining, is useful to discover distribution patterns in the underlying data. Clustering algorithms usually employ a distance metric based (e.g., euclidean) similarity measure in order to partition the database such that data points in the same partition are more similar than points in different partitions. In this paper, we study clustering algorithms for data with boolean and categorical attributes. We show that traditional clustering algorithms that use distances between points for clustering are not appropriate for boolean and categorical attributes. Instead, we propose a novel concept of links to measure the similarity/proximity between a pair of data points. We develop a robust hierarchical clustering algorithm ROCK that employs links and not distances when merging clusters.
Concentration Of Measure And Isoperimetric Inequalities In Product Spaces
, 1995
"... . The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product# N of probability spaces has measure at least one half, "most" of the points of# N are "close" to A. We proceed to a systematic exploration of this phenomenon. The meaning ..."
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Cited by 383 (4 self)
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. The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product# N of probability spaces has measure at least one half, "most" of the points of# N are "close" to A. We proceed to a systematic exploration of this phenomenon. The meaning of the word "most" is made rigorous by isoperimetrictype inequalities that bound the measure of the exceptional sets. The meaning of the work "close" is defined in three main ways, each of them giving rise to related, but di#erent inequalities. The inequalities are all proved through a common scheme of proof. Remarkably, this simple approach not only yields qualitatively optimal results, but, in many cases, captures near optimal numerical constants. A large number of applications are given, in particular to Percolation, Geometric Probability, Probability in Banach Spaces, to demonstrate in concrete situations the extremely wide range of application of the abstract tools. AMS Classification numbers: Primary 60E15, 28A35, 60G99; Secondary 60G15, 68C15. Typeset by A M ST E X 1 2 M. TALAGRAND Table of Contents I.
Results 1  10
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