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The asymmetric matrix partition problem
, 2012
"... An instance of the asymmetric matrix partition problem consists of a matrix A ∈ R n×m + and a probability distribution p over its columns. The goal is to find a partition scheme that maximizes the resulting partition value. A partition scheme S = {S1,..., Sn} consists of a partition Si of [m] for e ..."
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Cited by 3 (0 self)
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An instance of the asymmetric matrix partition problem consists of a matrix A ∈ R n×m + and a probability distribution p over its columns. The goal is to find a partition scheme that maximizes the resulting partition value. A partition scheme S = {S1,..., Sn} consists of a partition Si of [m
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 502 (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
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 547 (12 self)
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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
Partitioning of Unstructured Problems for Parallel Processing
, 1991
"... Many large scale computational problems are based on unstructured computational domains. Primary examples are unstructured grid calculations based on finite volume methods in computational fluid dynamics, or structural analysis problems based on finite element approximations. Here we will address th ..."
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Cited by 344 (16 self)
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a new decomposition algorithm will be discussed, which is based on the computation of an eigenvector of the Laplacian matrix associated with the graph. Numerical comparisons on large scale two and three dimensional problems demonstrate the superiority of the new spectral bisection algorithm.
The grid file: an adaptable, symmetric multikey file structure
 In Trends in Information Processing Systems, Proc. 3rd ECZ Conference, A. Duijvestijn and P. Lockemann, Eds., Lecture Notes in Computer Science 123
, 1981
"... Traditional file structures that provide multikey access to records, for example, inverted files, are extensions of file structures originally designed for singlekey access. They manifest various deficiencies in particular for multikey access to highly dynamic files. We study the dynamic aspects of ..."
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Cited by 426 (4 self)
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of tile structures that treat all keys symmetrically, that is, file structures which avoid the distinction between primary and secondary keys. We start from a bitmap approach and treat the problem of file design as one of data compression of a large sparse matrix. This leads to the notions of a grid
New spectral methods for ratio cut partition and clustering
 IEEE TRANS. ON COMPUTERAIDED DESIGN
, 1992
"... Partitioning of circuit netlists is important in many phases of VLSI design, ranging from layout to testing and hardware simulation. The ratio cut objective function [29] has received much attention since it naturally captures both mincut and equipartition, the two traditional goals of partitionin ..."
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Cited by 296 (17 self)
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of partitioning. In this paper, we show that the second smallest eigenvalue of a matrix derived from the netlist gives a provably good approximation of the optimal ratio cut partition cost. We also demonstrate that fast Lanczostype methods for the sparse symmetric eigenvalue problem are a robust basis
Spectral Partitioning of Random Graphs
, 2001
"... Problems such as bisection, graph coloring, and clique are generally believed hard in the worst case. However, they can be solved if the input data is drawn randomly from a distribution over graphs containing acceptable solutions. In this paper we show that a simple spectral algorithm can solve all ..."
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Cited by 165 (3 self)
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three problems above in the average case, as well as a more general problem of partitioning graphs based on edge density. In nearly all cases our approach meets or exceeds previous parameters, while introducing substantial generality. We apply spectral techniques, using foremost the observation
Algorithms for Parallel Memory I: TwoLevel Memories
, 1992
"... We provide the first optimal algorithms in terms of the number of input/outputs (I/Os) required between internal memory and multiple secondary storage devices for the problems of sorting, FFT, matrix transposition, standard matrix multiplication, and related problems. Our twolevel memory model is n ..."
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Cited by 235 (27 self)
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We provide the first optimal algorithms in terms of the number of input/outputs (I/Os) required between internal memory and multiple secondary storage devices for the problems of sorting, FFT, matrix transposition, standard matrix multiplication, and related problems. Our twolevel memory model
Improved bounds for mixing rates of Markov chains and multicommodity flow
 Combinatorics, Probability and Computing
, 1992
"... The paper is concerned with tools for the quantitative analysis of finite Markov chains whose states are combinatorial structures. Chains of this kind have algorithmic applications in many areas, including random sampling, approximate counting, statistical physics and combinatorial optimisation. The ..."
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Cited by 205 (8 self)
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viewed as a graph. The bound gives sharper estimates for the mixing rate of several important complex Markov chains. As a result, improved bounds are obtained for the runtimes of randomised approximation algorithms for various problems, including computing the permanent of a 01 matrix, counting
Spectral Relaxation for Kmeans Clustering
, 2001
"... The popular Kmeans clustering partitions a data set by minimizing a sumofsquares cost function. A coordinate descend method is then used to find local minima. In this paper we show that the minimization can be reformulated as a trace maximization problem associated with the Gram matrix of the dat ..."
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Cited by 198 (27 self)
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The popular Kmeans clustering partitions a data set by minimizing a sumofsquares cost function. A coordinate descend method is then used to find local minima. In this paper we show that the minimization can be reformulated as a trace maximization problem associated with the Gram matrix
Results 1  10
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