A parallel graph partitioning algorithm for a message-passing multiprocessor

  • John R. Gilbert
  • Earl Zmijewski
Session 6A: Problem Mapping And Scheduling
Part of the Lecture Notes in Computer Science book series (LNCS, volume 297)


Cholesky Factorization Grid Graph Black Vertex Adjacency List Wide Separator 
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  1. [1]
    Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley Publishing Company, 1974.Google Scholar
  2. [2]
    R. M. Chamberlain. An algorithm for LU factorization with partial pivoting on the hypercube. Technical Report CCS 86/11, Chr. Michelsen Institute, 1986.Google Scholar
  3. [3]
    R. M. Chamberlain and M. J. D. Powell. QR factorization for linear least squares problems on the hypercube. Technical Report CCS 86/10, Chr. Michelsen Institute, 1986.Google Scholar
  4. [4]
    T. H. Dunigan. A message-passing multiprocessor simulator. Technical Report ORNL/TM-9966, Oak Ridge National Laboratory, 1986.Google Scholar
  5. [5]
    G. C. Everstine. A comparison of three resequencing algorithms for the reduction of matrix profile and wave front. International Journal for Numerical Methods in Engineering, 14:837–853, 1979.Google Scholar
  6. [6]
    Tse-yun Feng. A survey of interconnection networks. IEEE Computer, 12:12–27, 1981.Google Scholar
  7. [7]
    Geoffrey C. Fox and Steve W. Otto. Concurrent computation and the theory of complex systems. Technical Report CALT-68-1343, California Institute of Technology, 1986.Google Scholar
  8. [8]
    Alan George, Michael T. Heath, Joseph Liu, and Esmond Ng. Sparse Cholesky factorization on a local-memory multiprocessor. Technical Report ORNL/TM-9962, Oak Ridge National Laboratory, 1986.Google Scholar
  9. [9]
    Alan George and Joseph W. H. Liu. An automatic nested dissection algorithm for irregular finite element problems. SIAM Journal on Numerical Analysis, 15:1053–1069, 1978.Google Scholar
  10. [10]
    Alan George and Joseph W. H. Liu. Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall, 1981.Google Scholar
  11. [11]
    Alan George, Joseph W. H. Liu, and Esmond Ng. Communication results for parallel sparse Cholesky factorization on a hypercube. Submitted to Parallel Computing, 1987.Google Scholar
  12. [12]
    John R. Gilbert and Robert Endre Tarjan. The analysis of a nested dissection algorithm. To appear in Numerische Mathematik, 1987.Google Scholar
  13. [13]
    John Russell Gilbert. Graph Separator Theorems and Sparse Gaussian Elimination. Ph.D. thesis, Stanford University, 1980.Google Scholar
  14. [14]
    B. W. Kernighan and S. Lin. An efficient heuristic procedure for partitioning graphs. The Bell System Technical Journal, 49:291–307, 1970.Google Scholar
  15. [15]
    Charles E. Leiserson. Area-efficient graph layouts (for VLSI). In Proceedings of the 21st Annual Symposium on Foundations of Computer Science, pages 270–281, 1980.Google Scholar
  16. [16]
    Richard J. Lipton, Donald J. Rose, and Robert Endre Tarjan. Generalized nested dissection. SIAM Journal on Numerical Analysis, 16:346–358, 1979.Google Scholar
  17. [17]
    Richard J. Lipton and Robert Endre Tarjan. Applications of a planar separator theorem. SIAM Journal on Computing, 9:615–627, 1980.Google Scholar
  18. [18]
    Joseph W. H. Liu. Computational models and task scheduling for parallel sparse Cholesky factorization. Parallel Computing, 3:327–342, 1986.Google Scholar
  19. [19]
    Joseph W. H. Liu. Equivalent sparse matrix reordering by elimination tree rotations. Technical Report CS-86-12, York University, 1986.Google Scholar
  20. [20]
    Joseph W. H. Liu. The solution of mesh equations on a parallel computer. Technical Report, University of Waterloo, 1974.Google Scholar
  21. [21]
    Frans J. Peters. MIMD machines and sparse linear equations. In Highly parallel computers for numerical and signal processing applications: Proceedings of a working conference of the International Federation for Information Processing Working Group 10.3, North-Holland, 1986.Google Scholar
  22. [22]
    Frans J. Peters. Parallel pivoting algorithms for sparse symmetric matrices. Parallel Computing, 1:99–110, 1984.Google Scholar
  23. [23]
    Donald J. Rose, Robert Endre Tarjan, and George S. Leuker. Algorithmic aspects of vertex elimination on graphs. SIAM Journal on Computing, 5:266–283, 1976.Google Scholar
  24. [24]
    Earl Zmijewski. Sparse Cholesky Factorization on a Multiprocessor. Ph.D. thesis, Cornell University, 1987.Google Scholar
  25. [25]
    Earl Zmijewski and John R. Gilbert. A parallel algorithm for large sparse symbolic and numeric Cholesky factorization on a multiprocessor. Technical Report 86–733, Cornell University, 1986.Google Scholar
  26. [26]
    Earl Zmijewski and John R. Gilbert. A parallel algorithm for sparse symbolic Cholesky factorization on a multiprocessor. To appear in Parallel Computing.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • John R. Gilbert
    • 1
  • Earl Zmijewski
    • 1
  1. 1.Department of Computer ScienceCornell UniversityIthaca

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