Extended parallelism in the Groebner basis algorithm

Abstract: "This paper presents a new parallel algorithm to compute Gröbner 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 below. I also discuss the design and implementation approaches used to construct an efficient version of this algorithm."