Parallel ordering using edge contraction

Parallel Computing

Volumn 23, Issue 8, 1997, Pages 1045-1067

  Raghavan, Padma ^a  

^a University of Tennessee Knoxville   (United States)

Author keywords

Fill in; Nested dissection; Ordering; Parallel algorithms; Parallel nested dissection; Sparse linear systems; Sparse matrix factorization

Indexed keywords

COMPUTATIONAL COMPLEXITY; GRAPH THEORY; HEURISTIC METHODS; MATRIX ALGEBRA; PARALLEL PROCESSING SYSTEMS;

PARALLEL CONTRACTED ORDERING; PARALLEL NESTED DISSECTION; SPARSE LINEAR SYSTEMS;

PARALLEL ALGORITHMS;

EID: 0031209254     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-8191(97)00018-5     Document Type: Article

References (34)

1. P. Amestoy, T. Davis, I. Duff, An approximate minimum degree ordering algorithm, Tech. Rep. CS-94-039, Department of Computer Science, Univ. of Florida, Gainsville, FL, 1994, SIAM J. Matrix Anal. Appl., to appear.
2. C. Ashcraft, J.W.H. Liu, Robust orderings of sparse matrices using multisection, Tech. Rep. ISSTECH-96-002, Boeing Computer Services, Seattle, WA, 1996.
3. S.T. Barnard, H. Simon, A fast multilevel implementation of recursive spectral bisection for partitioning unstructured meshes, in: R.F. Sincovec, D.E. Keyes, M.R. Leuze, L.R. Petzold, D.A. Reed (Eds.), Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, SIAM Publications, Philadelphia, PA, 1993, pp. 711-718.
4. S.T. Barnard, H. Simon, A parallel implementation of multilevel recursive spectral bisection for partitioning unstructured meshes, in: D.H. Bailey, P.E. Bjorstad, J.R. Gilbert, M.V. Mascagni, R.S. Schreiber, H.D. Simon, V.J. Torczon, L.T. Watson (Eds.), Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing, SIAM Publications, Philadelphia, PA, 1995, pp. 627-632.
5. M. Barnett, S. Gupta, D. Payne, L. Shuler, R. van de Geijn, J. Watts, Interprocessor collective communication library (InterCom), in Scalable High Performance Computing Conference, IEEE Computer Society Press, Los Alamitos, CA, 1994.
6. T.N. Bui, C. Jones, A heuristic for reducing fill in sparse matrix factorization, in: R.F. Sincovec, D.E. Keyes, M.R. Leuze, L.R. Petzold, D.A. Reed (Eds.), Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, SIAM Publications, Philadephia, PA, 1993, pp. 445-456.
7. E. Chu, A. George, J. Liu, E. Ng, SPARSPAK: Waterloo sparse matrix package user's guide for SPARSPAK-A, Tech. Rep. CS-84-36, Department of Computer Science, Univ. of Waterloo, Waterloo, Ontario, Canada, 1984.
8. I.S. Duff, A.M. Erisman, J.K. Reid, Direct Methods for Sparse Matrices, Clarendon Press, Oxford, 1986.
9. M.P.I. Forum, MPI: A message-passing interface standard, Tech. Rep. CS-94-230, Computer Science Dept., Univ. of Tennessee, Knoxville, April 1994.
10. J.A. George, Nested dissection of a regular finite element mesh, SIAM J. Numer. Anal. 10 (1973) 345-363.
11. J.A. George, J.W.-H. Liu, An automatic nested dissection algorithm for irregular finite element problems, SIAM J. Numer. Anal. 15 (1978) 1053-1069.
12. J.A. George, J.W.-H. Liu, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall Inc., Englewood Cliffs, NJ, 1981.
13. J.A. George, J.W.-H. Liu, The evolution of the minimum degree ordering algorithm, SIAM Rev. 31 (1989) 1-19.
14. J.R. Gilbert, G.L. Miller, S.H. Teng, Geometric mesh partitioning: Implementation and experiments, Tech. Rep., Xerox Palo Alto Research Center, 1994.
15. J.R. Gilbert, E. Zmijewski, A parallel graph partitioning algorithm for a message-passing multiprocessor, Int. J. Parallel Program. 16 (1987) 427-449.
16. A. Gupta, Fast and effective algorithms for graph partitioning and sparse matrix ordering, Tech. Rep. RC-20496, IBM Research Division, T.J. Watson Research Center, Yorktown Heights, NY 10598, 1996.
17. M.T. Heath, E. Ng, B.W. Peyton, Parallel algorithms for sparse linear systems, SIAM Rev. 33 (1991) 420-460.
18. M.T. Heath, P. Raghavan, Performance of a fully parallel sparse solver, in Scalable High Performance Computing Conference, IEEE Computer Society Press., Los Alamitos, CA, 1994, Int. J. Supercomputer Appl., to appear.
19. M.T. Heath, P. Raghavan, A Cartesian nested dissection algorithm, SIAM J. Matrix Anal. Appl. 16 (1995) 235-253.
20. B. Hendrickson, R. Leland, A multilevel algorithm for partitioning graphs. Tech. Rep. SAND93-1301, Sandia National Laboratories, Albuquerque, NM 87185, 1993.
21. B. Hendrickson, R. Leland, A user guide to Chaco, Tech. Rep. SAND92-1460, Sandia National Laboratories, Albuquerque, NM 87185, 1994.
22. B. Hendrickson, E. Rothberg, Improving the runtime and quality of nested dissection ordering, Tech. Rep., Sandia National Laboratories, Albuquerque, NM 87185, 1996.
23. G. Karypis, V. Kumar, METIS: Unstructured graph partitioning and sparse matrix ordering system, Tech. Rep., Department of Computer Science, University of Minnesota, Minneapolis, MN, 1995.
24. G. Karypis, V. Kumar, Parallel multilevel graph partitioning, Tech. Rep. 95-036., Department of Computer Science, University of Minnesota, Minneapolis, MN, May 1995.
25. B. Kernighan, S. Lin, An efficient heuristic for partitioning graphs, Bell Syst. Tech. J. 49 (1970) 291-308.
26. C.E. Leiserson, The network architecture of the connection machine CM-5, in: Fourth Annual ACP Symposium on Parallel Algorithms and Architectures, ACM Publications, 1992, pp. 272-285.
27. R.J. Lipton, D.J. Rose, R.E. Tarjan, Generalized nested dissection, SIAM J. Numer. Anal. 16 (1979) 346-358.
28. J.W.-H. Liu, Modification of the minimum degree algorithm by multiple elimination, ACM Trans. Math. Software 11 (1985) 141-153.
29. G. Miller, S. Teng, W. Thurston, S. Vavasis, Automatic mesh partitioning, in: Workshop on Sparse Matrix Computations: Graph Theory Issues and Algorithms, Institute for Mathematics and Its Applications, Springer-Verlag, 1992.
30. S.F. Nugent, The iPSC/2 direct-connect communication technology, in: Third Conference on Hypercubes, Concurrent Computers, and Applications, 1988, pp. 51-59.
31. A. Pothen, H.D. Simon, K.-P. Liou, Partitioning sparse matrices with eigenvectors of graphs, SIAM J. Matrix Anal. Appl. 11 (1990) 430-452.
32. S. Ranka and S. Sahni, Hypercubic Algorithms for Image Processing and Pattern Recognition, Springer-Verlag, New York, NY, 1990.
33. E. Rothberg, A parallel implementation of the multiple minimum degree heuristic. Presentation, Fifth Siam Conference on Applied Linear Algebra 1994, Snowbird, UT.
34. E. Zmijewski, Sparse Cholesky Factorization on a Multiprocessor, Ph.D. thesis, Department of Computer Science, Cornell University, August 1987.