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4,167
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
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Cited by 465 (1 self)
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which
Exact Algorithms for Maximum Acyclic Subgraph on a Superclass of Cubic Graphs
"... Abstract. Finding a maximum acyclic subgraph is on the list of problems that seem to be hard to tackle from a parameterized perspective. We develop two quite efficient algorithms (one is exact, the other parameterized) for (1, n)graphs, a class containing cubic graphs. The running times are O ∗ (1. ..."
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Cited by 2 (2 self)
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Abstract. Finding a maximum acyclic subgraph is on the list of problems that seem to be hard to tackle from a parameterized perspective. We develop two quite efficient algorithms (one is exact, the other parameterized) for (1, n)graphs, a class containing cubic graphs. The running times are O ∗ (1
Approximations For The Maximum Acyclic Subgraph Problem
 Information Processing Letters
, 1994
"... : Given a directed graph G = (V; A), the maximum acyclic subgraph problem is to compute a subset, A 0 , of arcs of maximum size or total weight so that G 0 = (V; A 0 ) is acyclic. We discuss several approximation algorithms for this problem. Our main result is an O(jAj + d 3 max ) algorithm ..."
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Cited by 17 (1 self)
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: Given a directed graph G = (V; A), the maximum acyclic subgraph problem is to compute a subset, A 0 , of arcs of maximum size or total weight so that G 0 = (V; A 0 ) is acyclic. We discuss several approximation algorithms for this problem. Our main result is an O(jAj + d 3 max ) algorithm
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 627 (44 self)
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as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar
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
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.
An introduction to variational methods for graphical models
 TO APPEAR: M. I. JORDAN, (ED.), LEARNING IN GRAPHICAL MODELS
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