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Ruling out PTAS for graph minbisection, dense ksubgraph, and bipartite clique
 SIAM J. Comput
"... Abstract Assuming that NP 6 ` "ffl?0 BPTIME(2nffl), we show that Graph MinBisection, Dense kSubgraph and Bipartite Clique have no Polynomial Time Approximation Scheme (PTAS). We give a reduction from the Minimum Distance of Code Problem (MDC). Starting with an instance of MDC, we build a Q ..."
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Cited by 56 (0 self)
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Abstract Assuming that NP 6 ` "ffl?0 BPTIME(2nffl), we show that Graph MinBisection, Dense kSubgraph and Bipartite Clique have no Polynomial Time Approximation Scheme (PTAS). We give a reduction from the Minimum Distance of Code Problem (MDC). Starting with an instance of MDC, we build a
The densest ksubgraph problem on clique graphs
 IN INTERNATIONAL COMBINATORICS, GEOMETRY AND COMPUTER SCIENCE CONFERENCE
, 2007
"... The Densest kSubgraph (DkS) problem asks for a kvertex subgraph of a given graph with the maximum number of edges. The problem is strongly NPhard, as a generalization of the well known Clique problem and we also know that it does not admit a Polynomial Time Approximation Scheme (PTAS). In this p ..."
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Cited by 8 (1 self)
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The Densest kSubgraph (DkS) problem asks for a kvertex subgraph of a given graph with the maximum number of edges. The problem is strongly NPhard, as a generalization of the well known Clique problem and we also know that it does not admit a Polynomial Time Approximation Scheme (PTAS
Approximation schemes, cliques, colors and densest subgraphs
"... Abstract. In this thesis we study the problem of finding the densest ksubgraph of a given graph G = (V, E). We present algorithms of polynomial time as well as approximation results on special graph classes. Analytically, we study polynomial time algorithms for the densest ksubgraph problem on wei ..."
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on weighted graphs of maximal degree two, on weighted trees even if the solution is disconnected, and on interval graphs with intersection only between two consecutive cliques. Moreover, we present a polynomial time approximation scheme for the densest ksubgraph problem on a star of cliques and a polynomial
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
Densest kSubgraph Approximation on Intersection Graphs
"... Abstract. We study approximation solutions for the densest ksubgraph problem (DSk) on several classes of intersection graphs. We adopt the concept of σquasi elimination orders, introduced by Akcoglu et al. [1], generalizing the perfect elimination orders for chordal graphs, and develop a simple O ..."
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Cited by 4 (0 self)
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Abstract. We study approximation solutions for the densest ksubgraph problem (DSk) on several classes of intersection graphs. We adopt the concept of σquasi elimination orders, introduced by Akcoglu et al. [1], generalizing the perfect elimination orders for chordal graphs, and develop a simple
An introduction to variational methods for graphical models
 TO APPEAR: M. I. JORDAN, (ED.), LEARNING IN GRAPHICAL MODELS
"... ..."
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.
Results 1  10
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