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PMRSB: parallel multilevel recursive spectral bisection

Published:08 December 1995Publication History

ABSTRACT

The design of a parallel implementation of multilevel recursive spectral bisection on the Cray T3D is described. The code is intended to be fast enough to enable dynamic repartitioning of adaptive meshes and to partition meshes that are too large for workstations. Two innovations in the implementation are recursive asynchronous task teams and a parallel version of the multilevel accelerator. A performance improvement of a factor of 140 over the best available serial implementation is demonstrated.

References

  1. 1.S. T. Barnard and H. D. Simon, 'Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems', Concurrency: Practice and Experience, Vol. 6, No. 2, 101-117 (1994).Google ScholarGoogle ScholarCross RefCross Ref
  2. 2.S. T. Barnard, A. Pothen, and H. D. Simon, 'A spectral algorithm for envelope reduction of sparse matrices', Proceedings of SU- PERCOMPUTING '93, 493-502, Portland, Oregon, (November 15-19, 1993). Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. 3.E. D. Brooks III, B. C. Gorda, and Karen H. Warren, 'The Parallel C Preprocessor', Scientific Programming, Vol. 1, No. 1, 79-89 (1992).Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. 4.CMSSL For CM Fortran, Vol. II, version 3.2, Thinking Machines Corp., (1994).Google ScholarGoogle Scholar
  5. 5.P. Diniz, S. Plimpton, B. Hendrickson, and R. Leland, 'Parallel algorithms for dynamically partitioning unstructured grids', Proceeding of the Seventh SIAM Conference on Parallel Processing for Scientific Computing, 615-620 (1995).Google ScholarGoogle Scholar
  6. 6.M. Garey, D. Johnson, and L. Stockmeyer, 'Some simplified NP- complete graph problems', Theoretical Computer Science,1, 237-267 (1976).Google ScholarGoogle ScholarCross RefCross Ref
  7. 7.C. Lanczos, 'An iteration method for the solution of the eigenvalue problem of linear differential and integral operators', J. Res. Nat. Bur. Stand., 45, 255-282 (1950).Google ScholarGoogle ScholarCross RefCross Ref
  8. 8.M. Luby, 'A simple parallel algorithm for the maximal independent set problem', SIAM J. Comput., Vol. 15, No. 4, (1986). Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. 9.C. C. Paige and M. A. Saunders, 'Solution of sparse indefinite systems of linear equations', SIAM J. Numer. Anal., Vol. 12, 617-629 (1974).Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. 10.B. N. Parlett, 'The Rayleigh quotient iteration and some generalizations for nonnormal matrices', Math Comp., 28(127), 679- 693 (1974).Google ScholarGoogle ScholarCross RefCross Ref
  11. 11.B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice Hall, Englewood Cliffs, New Jersey, 1980. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. 12.H. Gazit, 'Randomized parallel connectivity', in Synthesis of Parallel Applications, ed. by J. H. Reif, 197-214, Morgan Kaufmann Publishers, Inc., 1993.Google ScholarGoogle Scholar
  13. 13.H. Simon, 'Partitioning unstructured problems for parallel processing', Comput. Syst. Eng., 2(2/3), 135-148 (1991).Google ScholarGoogle ScholarCross RefCross Ref
  14. 14.Numerical Recipes in C, Second Edition, W. H. Press, S. A. Teukolosky, W. T. Vetterling, and B. P. Flannery, Cambridge University Press, 1994.Google ScholarGoogle Scholar

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                        cover image ACM Conferences
                        Supercomputing '95: Proceedings of the 1995 ACM/IEEE conference on Supercomputing
                        December 1995
                        875 pages
                        ISBN:0897918169
                        DOI:10.1145/224170
                        • Chairman:
                        • Sid Karin

                        Copyright © 1995 ACM

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                        Association for Computing Machinery

                        New York, NY, United States

                        Publication History

                        • Published: 8 December 1995

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                        Supercomputing '95 Paper Acceptance Rate69of241submissions,29%Overall Acceptance Rate1,516of6,373submissions,24%

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