A Hypergraph Partitioning Model for Profile Minimization

In this paper, the aim is to symmetrically permute the rows and columns of a given sparse symmetric matrix so that the profile of the permuted matrix is minimized. We formulate this permutation pro...

[1]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .

[2]  Desmond J. Higham,et al.  Unravelling small world networks , 2003 .

[3]  Erik G. Bomany,et al.  A Multilevel Algorithm for Reducing the Envelope of Sparse Matrices , 1996 .

[4]  Sanderson L. Gonzaga de Oliveira,et al.  A Systematic Review of Heuristics for Profile Reduction of Symmetric Matrices , 2015, ICCS.

[5]  Aurelio R. L. Oliveira,et al.  Influence of matrix reordering on the performance of iterative methods for solving linear systems arising from interior point methods for linear programming , 2017, Math. Methods Oper. Res..

[6]  A. Pothen,et al.  Two improved algorithms for envelope and wavefront reduction , 1997 .

[7]  Hayder Radha,et al.  Graph entropy rate minimization and the compressibility of undirected binary graphs , 2012, 2012 IEEE Statistical Signal Processing Workshop (SSP).

[8]  Jennifer A. Scott,et al.  Implementing Hager's exchange methods for matrix profile reduction , 2002, TOMS.

[9]  Long Chen INTRODUCTION TO FINITE ELEMENT METHODS , 2003 .

[10]  Wei-Pai Tang,et al.  Ordering Methods for Preconditioned Conjugate Gradient Methods Applied to Unstructured Grid Problems , 1992, SIAM J. Matrix Anal. Appl..

[11]  J. Reid,et al.  ORDERING SYMMETRIC SPARSE MATRICES FOR SMALL PROFILE , 1999 .

[12]  Ümit V. Çatalyürek,et al.  Hypergraph-Partitioning-Based Decomposition for Parallel Sparse-Matrix Vector Multiplication , 1999, IEEE Trans. Parallel Distributed Syst..

[13]  S. Sloan An algorithm for profile and wavefront reduction of sparse matrices , 1986 .

[14]  John Reid,et al.  Ordering symmetric sparse matrices for small profile and wavefront , 1999 .

[15]  P. Grindrod Range-dependent random graphs and their application to modeling large small-world Proteome datasets. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  John G. Lewis Implementation of the Gibbs-Poole-Stockmeyer and Gibbs-King Algorithms , 1982, TOMS.

[17]  Jaco van de Pol,et al.  Bandwidth and Wavefront Reduction for Static Variable Ordering in Symbolic Reachability Analysis , 2016, NFM.

[18]  Michael B. Giles,et al.  Renumbering unstructured grids to improve the performance of codes on hierarchical memory machines , 1997 .

[19]  I. Duff,et al.  The effect of ordering on preconditioned conjugate gradients , 1989 .

[20]  Enver Kayaaslan,et al.  A Recursive Bipartitioning Algorithm for Permuting Sparse Square Matrices into Block Diagonal Form with Overlap , 2013, SIAM J. Sci. Comput..

[21]  Cevdet Aykanat,et al.  A Recursive Hypergraph Bipartitioning Framework for Reducing Bandwidth and Latency Costs Simultaneously , 2017, IEEE Transactions on Parallel and Distributed Systems.

[22]  Jinjiang Yuan,et al.  Profile minimization problem for matrices and graphs , 1994 .

[23]  JOSEP DÍAZ,et al.  A survey of graph layout problems , 2002, CSUR.

[24]  Timothy A. Davis,et al.  A survey of direct methods for sparse linear systems , 2016, Acta Numerica.

[25]  Norman E. Gibbs,et al.  Algorithm 509: A Hybrid Profile Reduction Algorithm [F1] , 1976, TOMS.

[26]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[27]  J. A. George Computer implementation of the finite element method , 1971 .

[28]  Prabhakar Raghavan,et al.  Sparse matrix reordering schemes for browsing hypertext , 1996 .

[29]  G. O. Chagas,et al.  An evaluation of reordering algorithms to reduce the computational cost of the incomplete Cholesky-conjugate gradient method , 2018 .

[30]  William W. Hager,et al.  Minimizing the Profile of a Symmetric Matrix , 2001, SIAM J. Sci. Comput..

[31]  Andrew Lumsdaine,et al.  A comparison of vertex ordering algorithms for large graph visualization , 2007, 2007 6th International Asia-Pacific Symposium on Visualization.

[32]  Jennifer A. Scott,et al.  A Multilevel Algorithm for Wavefront Reduction , 2001, SIAM J. Sci. Comput..

[33]  William G. Poole,et al.  An algorithm for reducing the bandwidth and profile of a sparse matrix , 1976 .

[34]  H. D. Simon,et al.  A spectral algorithm for envelope reduction of sparse matrices , 1993, Supercomputing '93. Proceedings.

[35]  Wei Xue,et al.  Performance modeling and optimization of sparse matrix-vector multiplication on NVIDIA CUDA platform , 2011, The Journal of Supercomputing.

[36]  Cevdet Aykanat,et al.  Improving performance of sparse matrix dense matrix multiplication on large-scale parallel systems , 2016, Parallel Comput..

[37]  Iain S. Duff,et al.  MA57---a code for the solution of sparse symmetric definite and indefinite systems , 2004, TOMS.

[38]  LONG CHEN INTRODUCTION TO FINITE ELEMENT METHODS ON ELLIPTIC EQUATIONS , 2013 .

[39]  Wei-Pai Tang,et al.  Weighted graph based ordering techniques for preconditioned conjugate gradient methods , 1995 .

[40]  Timothy A. Davis,et al.  The university of Florida sparse matrix collection , 2011, TOMS.

[41]  AykanatCevdet,et al.  Hypergraph-Partitioning-Based Decomposition for Parallel Sparse-Matrix Vector Multiplication , 1999 .