Using domain decomposition to find graph bisectors

BIT Numerical Mathematics

Volumn 37, Issue 3, 1997, Pages 506-534

  Ashcraft, Cleve ^a   Liu, Joseph W H ^b  

^a BOEING COMPANY   (United States)

^b YORK UNIVERSITY   (Canada)

Author keywords

Bipartite graph matching; Domain decomposition; Graph bisectors; Nested dissection; Sparse matrix computation

Indexed keywords

EID: 0039893940     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510238     Document Type: Article

References (27)

1. C. Ashcraft, The domain/segment partition for the factorization of sparse symmetric positive definite matrices, Tech. Report ECA-TR-148, Boeing Computer Services, Seattle, WA, 1990.
2. C. Ashcraft, Compressed graphs and the minimum degree algorithm, SIAM J. Sci. Comput., 16 (1995), pp. 1404-1411.
3. C. Ashcraft and J. W. H. Liu, Applications of the Dulmage-Mendelsohn decomposition and network flow to graph bisection improvement, Technical Report ISSTECH-96-017, Boeing Computer Services, Seattle, WA, 1996, submitted to SIAM J. Matrix Anal.
4. C. Ashcraft and J. W. H. Liu, A partition improvement algorithm for generalized nested dissection, Technical Report BCSTECH-94-020, Boeing Computer Services, Seattle, WA, 1994.
5. C. Ashcraft and J. W. H. Liu, Robust ordering of sparse matrices using multisection, Tech. Report ISSTECH-96-002, Boeing Information and Support Services, Seattle, WA, 1996, submitted to SIAM J. Matrix Anal.
6. C. Ashcraft and J. W. H. Liu, Generalized nested dissection: some recent progress, in Fifth SIAM Conference on Applied Linear Algebra, Snowbird, Utah, June 18, 1994.
7. T. Bui and C. Jones, Finding good approximate vertex and edge partitions is NP-hard, Information Processing Letters, 42 (1992), pp. 153-159.
8. T. Bui and C. Jones, A heuristic for reducing fill-in in sparse matrix factorization, in Proceedings of the Sixth SIAM Conference on Parallel Processing, pp. 445-452, 1993.
9. A. C. Damhaug, Sparse Solution of Finite Element Equations, Ph.D. thesis, The Norwegian Institute of Technology, Trondheim, Norway, 1992.
10. C. M. Fiduccia and R. M. Mattheyses, A linear-time heuristic for improving network partition, In ACM IEEE Proc. 19th Design Automation Conference, pp. 175-181, Las Vegas, Nevada, June 14-16, 1982.
11. J. A. George, Nested dissection of a regular finite element mesh, SIAM J. Numer. Anal., 10 (1973), pp. 345-363.
12. J. A. George and J. W. H. Liu, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981.
13. J. A. George and J. W. H. Liu, The evolution of the minimum degree ordering algorithm, SIAM Review, 31 (1989), pp. 1-19.
14. T. Goehring and Y. Saad, Heuristic algorithms for automatic graph partitioning, Tech. Report, Department of Computer Science, University of Minnesota, MN, 1995.
15. B. Hendrickson and R. Leland. The Chaco user's guide, Tech. Report SAND93-2339, Sandia National Laboratories, Albuquerque, NM, 1993.
16. B. Hendrickson and R. Leland, An improved spectral graph partitioning algorithm for mapping parallel computations, SIAM J. Sci. Comput., 16 (1995), pp. 452-469.
17. G. Karypis and V. Kumar, Analysis of multilevel graph partitioning, Tech. Report TR 95-037, Department of Computer Science, University of Minnesota, MN, 1995.
18. G. Karypis and V. Kumar, A fast and high quality multilevel scheme for partitioning irregular graphs, Technical Report TR 95-035, Department of Computer Science, University of Minnesota, MN, 1995.
19. G. Karypis and V. Kumar, Metis: Unstructured graph partitioning and sparse matrix ordering system, Tech. Report, Department of Computer Science, University of Minnesota, MN, 1995.
20. B. W. Kernighan and S. Lin, An efficient heuristic procedure for partitioning graphs, Bell System Technical Journal, 49 (1970), pp. 291-307.
21. C. E. Leiserson and J. G. Lewis, Orderings for parallel sparse symmetric factorization, in Parallel Processing for Scientific Computing, (1989), pp. 27-31.
22. J. W. H. Liu, A graph partitioning algorithm by node separators, ACM Trans. Math Software, 15 (1989), pp. 198-219.
23. A. Pothen and C. Fan, Computing the block triangular form of a sparse matrix, ACM Trans. Math Software, 16 (1990), pp. 303-324.
24. A. Pothen, H. Simon, and K. P. Liou, Partitioning sparse matrices with eigenvectors of graphs, SIAM J. Matrix Anal. Applic., 11 (1990), pp. 430-452.
25. F. P. Preparata and M. I. Shamos, Computational Geometry: An Introduction, Springer-Verlag, 1985.
26. J. D. Ullman, Computational Aspects of VLSI, Computer Science Press, Rockville, MD, 1984.
27. L. Wang, Spectral nested dissection, Ph.D. thesis, The Pennsylvania State University, Department of Computer Science and Engineering, University Park, PA, 1994.