Extended Parallelism Basis Algorithm
Stephen Schwab · 1992
in the Gr6bner This paper presents a new parallel implementation to compute Gr6bner bases utilizing two different forms of parallelism. A coarse-grain technique developed by Jean-Phillipe Vidal expands and reduces S-polynomials in parallel. A fine-grain 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. KEY WORDS: Parallel algorithms; shared memory multiprocessors; Gr6bner bases; computer algebra.