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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 ..."
Abstract

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
Spectral partitioning with multiple eigenvectors
 DISCRETE APPLIED MATHEMATICS
, 1999
"... The graph partitioning problem is to divide the vertices of a graph into disjoint clusters to minimize the total cost of the edges cut by the clusters. A spectral partitioning heuristic uses the graph’s eigenvectors to construct a geometric representation of the graph (e.g., linear orderings) which ..."
Abstract

Cited by 37 (0 self)
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The graph partitioning problem is to divide the vertices of a graph into disjoint clusters to minimize the total cost of the edges cut by the clusters. A spectral partitioning heuristic uses the graph’s eigenvectors to construct a geometric representation of the graph (e.g., linear orderings) which
Spectral Partitioning: The More Eigenvectors, the Better
 PROC. ACM/IEEE DESIGN AUTOMATION CONF
, 1995
"... The graph partitioning problem is to divide the vertices of a graph into disjoint clusters to minimize the total cost of the edges cut by the clusters. A spectral partitioning heuristic uses the graph's eigenvectors to construct a geometric representation of the graph (e.g., linear orderings) w ..."
Abstract

Cited by 75 (3 self)
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The graph partitioning problem is to divide the vertices of a graph into disjoint clusters to minimize the total cost of the edges cut by the clusters. A spectral partitioning heuristic uses the graph's eigenvectors to construct a geometric representation of the graph (e.g., linear orderings
Geometric Spectral Partitioning
, 1995
"... We investigate a new method for partitioning a graph into two equalsized pieces with few connecting edges. We combine ideas from two recently suggested partitioning algorithms, spectral bisection (which uses an eigenvector of a matrix associated with the graph) and geometric bisection (which applie ..."
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Cited by 16 (2 self)
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We investigate a new method for partitioning a graph into two equalsized pieces with few connecting edges. We combine ideas from two recently suggested partitioning algorithms, spectral bisection (which uses an eigenvector of a matrix associated with the graph) and geometric bisection (which
Spectral Partitioning for Boundary Estimation
 IN J.S. BOSWELL(ED.) PROC. OF INT. JOINT CONF. NEURAL NETWORKS, WASHINGTON DC, #0733
, 1999
"... We propose a spectral technique for analysing intermediate feature space of multiple classifier decisions, which enables a separable subset of patterns to be extracted. The method is applied to finding a set of patterns that are inconsistently classified, a random subset of which is left out of the ..."
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Cited by 2 (2 self)
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We propose a spectral technique for analysing intermediate feature space of multiple classifier decisions, which enables a separable subset of patterns to be extracted. The method is applied to finding a set of patterns that are inconsistently classified, a random subset of which is left out
Spectral Partitioning for Boundary Estimation
 In J.S. Boswell(ed.) Proc. of Int. Joint Conf. Neural Networks, Washington DC, #0733
, 1999
"... We propose a spectral technique for analysing intermediate feature space of multiple classifier decisions, which enables a separable subset of patterns to be extracted. The method is applied to finding a set of patterns that are inconsistently classified, a random subset of which is left out of the ..."
Abstract
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We propose a spectral technique for analysing intermediate feature space of multiple classifier decisions, which enables a separable subset of patterns to be extracted. The method is applied to finding a set of patterns that are inconsistently classified, a random subset of which is left out
Spectral partitioning works: planar graphs and finite element meshes, in:
 Proceedings of the 37th Annual Symposium on Foundations of Computer Science,
, 1996
"... Abstract Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to wo ..."
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Cited by 201 (10 self)
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Abstract Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment
Spectral Partitioning for Structure from Motion
"... We propose a spectral partitioning approach for largescale optimization problems, specifically structure from motion. In structure from motion, partitioning methods reduce the problem into smaller and better conditioned subproblems which can be efficiently optimized. Our partitioning method uses on ..."
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Cited by 17 (3 self)
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We propose a spectral partitioning approach for largescale optimization problems, specifically structure from motion. In structure from motion, partitioning methods reduce the problem into smaller and better conditioned subproblems which can be efficiently optimized. Our partitioning method uses
Multilevel Spectral Partitioning of Unstructured Grids
"... INTRODUCTION The graph partitioning problem is an important component of parallel computing (e.g. for constructing subdomains in domain decomposition methods) and as a result, many partitioning methods and associated sophisticated software packages have been developed recently. The goal in partitio ..."
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in partitioning a graph is to find a separator which bisects the the graph while minimizing the number of edges cut. Such partitioners include algorithms based on greedy, coordinate, inertial, multilevel spectral and graph bisection. However, there is usually an unavoidable tradeoff between quality and speed
Spectral Partitioning for Structure from Motion
"... We propose a spectral partitioning approach for largescale optimization problems, specifically structure from motion. In structure from motion, partitioning methods reduce the problem into smaller and better conditioned subproblems which can be efficiently optimized. Our partitioning method uses on ..."
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We propose a spectral partitioning approach for largescale optimization problems, specifically structure from motion. In structure from motion, partitioning methods reduce the problem into smaller and better conditioned subproblems which can be efficiently optimized. Our partitioning method uses
Results 1  10
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