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49
The University of Florida sparse matrix collection
 NA DIGEST
, 1997
"... The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural enginee ..."
Abstract

Cited by 301 (15 self)
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The University of Florida Sparse Matrix Collection is a large, widely available, and actively growing set of sparse matrices that arise in real applications. Its matrices cover a wide spectrum of problem domains, both those arising from problems with underlying 2D or 3D geometry (structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, networks and graphs, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, and power networks). The collection meets a vital need that artificiallygenerated matrices cannot meet, and is widely used by the sparse matrix algorithms community for the development and performance evaluation of sparse matrix algorithms. The collection includes software for accessing and managing the collection, from MATLAB, Fortran, and C.
Multilevel algorithms for multiconstraint graph partitioning
 In Proceedings of Supercomputing
, 1998
"... ( kirk, karypis, kumar) @ cs.umn.edu ..."
Highly scalable parallel algorithms for sparse matrix factorization
 IEEE Transactions on Parallel and Distributed Systems
, 1994
"... In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze their performance and scalability, and present experimental results for up to 1024 processors on a Cray T3D parallel computer. Through our analysis and experimental results, we demonstrate that our algo ..."
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Cited by 116 (29 self)
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In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze their performance and scalability, and present experimental results for up to 1024 processors on a Cray T3D parallel computer. Through our analysis and experimental results, we demonstrate that our algorithm substantially improves the state of the art in parallel direct solution of sparse linear systems—both in terms of scalability and overall performance. It is a well known fact that dense matrix factorization scales well and can be implemented efficiently on parallel computers. In this paper, we present the first algorithm to factor a wide class of sparse matrices (including those arising from two and threedimensional finite element problems) that is asymptotically as scalable as dense matrix factorization algorithms on a variety of parallel architectures. Our algorithm incurs less communication overhead and is more scalable than any previously known parallel formulation of sparse matrix factorization. Although, in this paper, we discuss Cholesky factorization of symmetric positive definite matrices, the algorithms can be adapted for solving sparse linear least squares problems and for Gaussian elimination of diagonally dominant matrices that are almost symmetric in structure. An implementation of our sparse Cholesky factorization algorithm delivers up to 20 GFlops on a Cray T3D for mediumsize structural engineering and linear programming problems. To the best of our knowledge,
Improving MemorySystem Performance of Sparse MatrixVector Multiplication
 IBM Journal of Research and Development
, 1997
"... Sparse MatrixVector Multiplication is an important kernel that often runs inefficiently on superscalar RISC processors. This paper describe techniques that increase instructionlevel parallelism and improve performance. The techniques include reordering to reduce cache misses originally due to Das ..."
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Cited by 72 (0 self)
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Sparse MatrixVector Multiplication is an important kernel that often runs inefficiently on superscalar RISC processors. This paper describe techniques that increase instructionlevel parallelism and improve performance. The techniques include reordering to reduce cache misses originally due to Das et al., blocking to reduce load instructions, and prefetching to prevent multiple loadstore units from stalling simulteneously. The techniques improve performnance from about 40 Mflops (on a wellordered matrix) to over 100 Mflops on a 266 Mflops machine. The techniques are applicable to other superscalar RISC processors as well and have improved performance on a Sun UltraSparc I workstation, for example. 1 Introduction Sparse matrixvector multiplication is an important computational kernel in many iterative linear solvers (see [5], for example). Unfortunately, on many computers this kernel runs slowly relative to other numerical codes, such as dense matrix computations. This paper propos...
Graph partitioning for high performance scientific simulations. Computing Reviews 45(2
, 2004
"... ..."
Permuting Sparse Rectangular Matrices into BlockDiagonal Form
 SIAM Journal on Scientific Computing
, 2002
"... We investigate the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for solving the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. W ..."
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Cited by 57 (19 self)
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We investigate the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for solving the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. We propose bipartite graph and hypergraph models to represent the nonzero structure of a matrix, which reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning, respectively. Our experiments on a wide range of matrices, using stateoftheart graph and hypergraph partitioning tools MeTiS and PaToH, revealed that the proposed methods yield very effective solutions both in terms of solution quality and runtime.
Mesh Partitioning: a Multilevel Balancing and Refinement Algorithm
, 1998
"... Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. In this paper we present an enhancement o ..."
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Cited by 55 (22 self)
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Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. In this paper we present an enhancement of the technique which uses imbalance to achieve higher quality partitions. We also present a formulation of the KernighanLin partition optimisation algorithm which incorporates loadbalancing. The resulting algorithm is tested against a different but related stateofthe art partitioner and shown to provide improved results. Keywords: graphpartitioning, mesh partitioning, loadbalancing, multilevel algorithms. 1 Introduction The need for mesh partitioning arises naturally in many finite element (FE) and finite volume (FV) applications. Meshes composed of elements such as triangles or tetrahedra are often better suited than regularly structured grids for representing completely general ge...
Parallel Optimisation Algorithms for Multilevel Mesh Partitioning
 Parallel Comput
, 2000
"... Three parallel optimisation algorithms, for use in the context of multilevel graph partitioning of unstructured meshes, are described. The first, interface optimisation, reduces the computation to a set of independent optimisation problems in interface regions. The next, alternating optimisation, is ..."
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Cited by 45 (14 self)
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Three parallel optimisation algorithms, for use in the context of multilevel graph partitioning of unstructured meshes, are described. The first, interface optimisation, reduces the computation to a set of independent optimisation problems in interface regions. The next, alternating optimisation, is a restriction of this technique in which mesh entities are only allowed to migrate between subdomains in one direction. The third treats the gain as a potential field and uses the concept of relative gain for selecting appropriate vertices to migrate. The results are compared and seen to produce very high global quality partitions, very rapidly. The results are also compared with another partitioning tool and shown to be of higher quality although taking longer to compute. 2000 Elsevier Science B.V. All rights reserved.