Partitioning Rectangular Matrices for Parallel Processing

The authors are interested in partitioning sparse rectangular matrices for parallel processing. The partitioning problem has been well-studied in the square symmetric case, but the rectangular problem has received very little attention. They will formalize the rectangular matrix partitioning problem and discuss several methods for solving it. They will extend the spectral partitioning method for symmetric matrices to the rectangular case and compare this method to three new methods -- the alternating partitioning method and two hybrid methods. The hybrid methods will be shown to be best.

[1]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[2]  Alex Pothen,et al.  PARTITIONING SPARSE MATRICES WITH EIGENVECTORS OF GRAPHS* , 1990 .

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4]  Michael A. Saunders,et al.  LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares , 1982, TOMS.

[5]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[6]  Dianne P. O'Leary,et al.  Digital Image Compression by Outer Product Expansion , 1983, IEEE Trans. Commun..

[7]  Horst D. Simon,et al.  Partitioning of unstructured problems for parallel processing , 1991 .

[8]  Horst D. Simon,et al.  Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems , 1994, Concurr. Pract. Exp..

[9]  Franz Rendl,et al.  A computational study of graph partitioning , 1994, Math. Program..

[10]  Bruce Hendrickson,et al.  An Improved Spectral Graph Partitioning Algorithm for Mapping Parallel Computations , 1995, SIAM J. Sci. Comput..

[11]  Bruce Hendrickson,et al.  A Multi-Level Algorithm For Partitioning Graphs , 1995, Proceedings of the IEEE/ACM SC95 Conference.

[12]  Charles J. Alpert,et al.  Spectral Partitioning: The More Eigenvectors, The Better , 1995, 32nd Design Automation Conference.

[13]  Vipin Kumar,et al.  Parallel multilevel graph partitioning , 1996, Proceedings of International Conference on Parallel Processing.

[14]  Shang-Hua Teng,et al.  Spectral partitioning works: planar graphs and finite element meshes , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[15]  Bruce Hendrickson,et al.  Skewed Graph Partitioning , 1997, PP.

[16]  Tamara G. Kolda,et al.  Limited-memory matrix methods with applications , 1997 .

[17]  Tamara G. Kolda,et al.  Partitioning Sparse Rectangular Matrices for Parallel Computations of Ax and ATv , 1998, PARA.

[18]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[19]  Tamara G. Kolda,et al.  A semidiscrete matrix decomposition for latent semantic indexing information retrieval , 1998, TOIS.