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Multilevel Recursive Spectral Bisection
"... This thesis investigates a multilevel approach to a graph partitioning method calles spectral bisection. The main... ..."
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This thesis investigates a multilevel approach to a graph partitioning method calles spectral bisection. The main...
A Spectral Bisection Partitioning Method for Electric Power Network Applications *
"... Coherency, network/graph decomposition, spectral bisection partitioning, ..."
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Cited by 3 (0 self)
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Coherency, network/graph decomposition, spectral bisection partitioning,
PMRSB: Parallel Multilevel Recursive Spectral Bisection
 In Supercomputing
, 1995
"... The design of a parallel implementation of multilevel recursive spectral bisection on the Cray T3D is described. The code is intended to be fast enough to enable dynamic repartitioning of adaptive meshes and to partition meshes that are too large for workstations. Two innovations in the implementati ..."
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Cited by 40 (0 self)
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The design of a parallel implementation of multilevel recursive spectral bisection on the Cray T3D is described. The code is intended to be fast enough to enable dynamic repartitioning of adaptive meshes and to partition meshes that are too large for workstations. Two innovations
On The Optimality Of The Median Cut Spectral Bisection Graph Partitioning Method
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1997
"... Recursive Spectral Bisection is a heuristic technique for finding a minimum cut graph bisection. In it, the second eigenvector of the Laplacian of the graph is computed and from it a bisection is obtained. The most common method is to use the median of the components of the second eigenvector to ind ..."
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Cited by 22 (3 self)
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Recursive Spectral Bisection is a heuristic technique for finding a minimum cut graph bisection. In it, the second eigenvector of the Laplacian of the graph is computed and from it a bisection is obtained. The most common method is to use the median of the components of the second eigenvector
Parallel implementation of recursive spectral bisection on the Connection Machine CM5 system
, 1994
"... this paper, we present only an abbreviated description of the parallel implementation of the RSB algorithm, followed by two decomposition examples. Details of the implementation can be found in [4]. ..."
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this paper, we present only an abbreviated description of the parallel implementation of the RSB algorithm, followed by two decomposition examples. Details of the implementation can be found in [4].
ftp ejde.math.txstate.edu (login: ftp) SPECTRAL BISECTION ALGORITHM FOR SOLVING SCHRÖDINGER EQUATION USING UPPER AND LOWER SOLUTIONS
"... Abstract. This paper establishes a new criteria for obtaining a sequence of upper and lower bounds for the ground state eigenvalue of Schrödinger equation −∆ψ(r) + V (r)ψ(r) = Eψ(r) in N spatial dimensions. Based on this proposed criteria, we prove a new comparison theorem in quantum mechanics for ..."
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that the substitution of the lower(upper) bound of the eigenvalue in Schrödinger equation leads to an upper(lower) solution. Finally, two proposed iteration approaches lead to an exact convergent sequence of solutions. The first one uses RaielghRitz theorem. Meanwhile, the second approach uses a new numerical spectral
Unification of Spectral and Inertial Bisection
 GREEDY, PROHIBITION, AND REACTIVE HEURISTICS FOR GRAPH PARTITIONING 36
, 1994
"... We discuss algorithms for graph bisection which are relevant to the distribution of tasks, such as the elements and nodes of an unstructured mesh to the processors of a parallel computer. Starting with a cost function consisting of a part to ensure equal numbers of tasks for each processor, and a pa ..."
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Cited by 1 (0 self)
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part to minimize communication time between processors, we derive the spectral bisection method, which consists of finding an eigenvector of a large sparse matrix. Inertial bisection is derived as a statistical approximation from the spectral method, via the moments of the node density and moments
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.
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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to work extremely well. In this paper, we show that spectral partitioning methods work well on boundeddegree planar graphs and finite element meshesthe classes of graphs to which they are usually applied. While naive spectral bisection does not necessarily work, we prove that spectral partitioning
Results 1  10
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