Abstract
This paper presents a new parallel implementation to compute Gröbner bases utilizing two different forms of parallelism. A coarse-grain technique developed by Jean-Phillipe Vidal expands and reducesS-polynomials in parallel. A finegrain technique, proposed by Melenk and Neun, constructs a pipeline of processors to overlap execution of the reduction operations. A hybrid algorithm that outperforms both of the original approaches is presented. The combined algorithm requires the user to select the appropriate allocation of processors to the two styles of parallelism, and uses this static assignment throughout the computation. The paper also discusses the design and implementation approaches used to construct an efficient version of this algorithm.
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The author was partially supported by an NSF graduate fellowship. This research was sponsored in part by the Avionics Laboratory, Wright Research and Development Center, Aeronautical Systems Division (AFSC), U.S. Air Force, Wright-Patterson AFB, Ohio 45433-6543 under Contract F33615-90-C-1465, ARPA Order No. 7597 and in part by the National Science Foundation under grant CCR-87-226-33. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of the National Science Foundation or the U.S. government.
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Schwab, S.A. Extended parallelism in the Gröbner basis algorithm. Int J Parallel Prog 21, 39–66 (1992). https://doi.org/10.1007/BF01379314
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DOI: https://doi.org/10.1007/BF01379314