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A Buchberger Algorithm for distributed memory multi-processors

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Parallel Computation (ACPC 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 591))

Abstract

Gröbner Bases are a mathematical tool that has received considerable attention in recent years. Since the Buchberger Algorithm for computing these objects is expensive in both space and time, several attempts at parallelization have been made, with good results for shared-memory multiprocessors, but not for distributed memory machines. We present an algorithm that delivers substantial speedups on distributed memory multi-processors, and an incremental version of the algorithm which is suitable for use as the solver in a constraint logic language.

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References

  1. S. G. Akl. Parallel Sorting Algorithms. Notes and Reports in Computer Science and Applied Mathematics. Academic Press, 1985.

    Google Scholar 

  2. W. Boege, R. Gebauer, and H. Kredel. Some examples for solving systems of algebraic equations by calculating groebner bases. J. Symbolic Computation, 2(1):83–98, 1986.

    Google Scholar 

  3. E. M. Clarke, D. E. Long, S. Michaylov, S. A. Schwab, J. P. Vidal, and S. Kimura. Parallel Symbolic Computation Algorithms. Technical Report CMU-CS-90-182, Computer Science Department, Carnegie Mellon University, Oct. 1990.

    Google Scholar 

  4. D. Hawley and A. Aiba. Guarded Definite Clauses with Constraints — A Preliminary Report. Japan-Italy-Sweden Workshop on Logic Programming and Parallel Processing, Stockholm, Sweden, Aug. 1990.

    Google Scholar 

  5. K. Nakajima, Y. Inamura, N. Ichiyoshi, K. Rokusawa, and T. Chikayama. Distributed implementation of KL1 on the Multi-PSI/V2. In Proceedings of ICLP'89, pages 436–451, 1989.

    Google Scholar 

  6. C. G. Ponder. Evaluation of ‘Performance Enhancements’ in algebraic manipulation systems. In J. D. Dora and J. Fitch, editors, Computer Algebra and Parallelism, pages 51–74. Academic Press, 1990.

    Google Scholar 

  7. P. Senechaud. Implementation of a parallel algorithm to compute a Gröbner basis on Boolean polynomials. In J. D. Dora and J. Fitch, editors, Computer Algebra and Parallelism, pages 159–166. Academic Press, 1990.

    Google Scholar 

  8. K. Siegl. Gröbner Bases Computation in STRAND: A Case Study for Concurrent Symbolic Computation in Logic Programming Languages. Master's thesis, CAMP-LINZ, Nov. 1990.

    Google Scholar 

  9. K. Ueda and T. Chikayama. Design of the kernel language for the parallel inference machine. Computer Journal, December 1990. To appear.

    Google Scholar 

  10. J. P. Vidal. The Computation of Gröbner bases on a shared memory multi-processor. Technical Report CMU-CS-90-163, Computer Science Department, Carnegie Mellon University, Aug. 1990.

    Google Scholar 

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Hans P. Zima

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© 1992 Springer-Verlag Berlin Heidelberg

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Hawley, D.J. (1992). A Buchberger Algorithm for distributed memory multi-processors. In: Zima, H.P. (eds) Parallel Computation. ACPC 1991. Lecture Notes in Computer Science, vol 591. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55437-8_94

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  • DOI: https://doi.org/10.1007/3-540-55437-8_94

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55437-0

  • Online ISBN: 978-3-540-47073-1

  • eBook Packages: Springer Book Archive

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