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Approximation Schemes for Metric Bisection and Partitioning
, 2004
"... We design polynomial time approximation schemes (PTASs) for Metric BISECTION, i.e. dividing a given finite metric space into two halves so as to minimize or maximize the sum of distances across the cut. The method extends to partitioning problems with arbitrary size constraints. Our approximation sc ..."
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Cited by 7 (3 self)
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We design polynomial time approximation schemes (PTASs) for Metric BISECTION, i.e. dividing a given finite metric space into two halves so as to minimize or maximize the sum of distances across the cut. The method extends to partitioning problems with arbitrary size constraints. Our approximation
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
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Cited by 1173 (16 self)
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Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
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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to efficiently (i.e., in time linear in the number of vertices) construct partitions of the graph which corre...
Approximation Schemes for Metric Minimum Bisection and Partitioning
"... We design polynomial time approximation schemes (PTASs) for Metric MINBISECTION, i.e. dividing a given nite metric space into two halves so as to minimize the sum of distances across the cut. The method extends to partitioning problems with arbitrary size constraints. Our approximation schemes depe ..."
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We design polynomial time approximation schemes (PTASs) for Metric MINBISECTION, i.e. dividing a given nite metric space into two halves so as to minimize the sum of distances across the cut. The method extends to partitioning problems with arbitrary size constraints. Our approximation schemes
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 500 (0 self)
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divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a
Bundle Adjustment  A Modern Synthesis
 VISION ALGORITHMS: THEORY AND PRACTICE, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 555 (12 self)
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covered include: the choice of cost function and robustness; numerical optimization including sparse Newton methods, linearly convergent approximations, updating and recursive methods; gauge (datum) invariance; and quality control. The theory is developed for general robust cost functions rather than
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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and maximum stable set problems in perfect graphs, the maximum k partite subgraph problem in graphs, and va...
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 of the same cluster and comparatively few edges joining vertices of different clusters. Such
QSplat: A Multiresolution Point Rendering System for Large Meshes
, 2000
"... Advances in 3D scanning technologies have enabled the practical creation of meshes with hundreds of millions of polygons. Traditional algorithms for display, simplification, and progressive transmission of meshes are impractical for data sets of this size. We describe a system for representing and p ..."
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Cited by 500 (8 self)
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Advances in 3D scanning technologies have enabled the practical creation of meshes with hundreds of millions of polygons. Traditional algorithms for display, simplification, and progressive transmission of meshes are impractical for data sets of this size. We describe a system for representing and progressively displaying these meshes that combines a multiresolution hierarchy based on bounding spheres with a rendering system based on points. A single data structure is used for view frustum culling, backface culling, levelofdetail selection, and rendering. The representation is compact and can be computed quickly, making it suitable for large data sets. Our implementation, written for use in a largescale 3D digitization project, launches quickly, maintains a usersettable interactive frame rate regardless of object complexity or camera position, yields reasonable image quality during motion, and refines progressively when idle to a high final image quality. We have demonstrated the system on scanned models containing hundreds of millions of samples.
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