A parallel Gröbner factorizer

Abstract

We report on some experience with a parallel version of the Gröbner basis algorithm with factorization, implemented in the REDUCE package CALI [4]. It is based on a coarse grain parallel master-slave model with distributed memory. This model was realized on an HP workstation cluster both with a disk remote connection based on (ordinary) REDUCE [9] and the special PVM-based parallel REDUCE version of H. Melenk and W. Neun [7]. Our considerations focus on a detailed study of the practical time behaviour of the parallelized improved Gröbner factorization algorithm [5]. For well splitting examples, where the number of intermediate subproblems is large compared to the number of parallel processes available on the system (only for such examples this approach makes sense), we've got almost always a good load balance. Since even for the relative slow disk remote connection the results are encouraging, we conclude that with a fast and stable communication hard- and software one will obtain a serious speed up on such problems compared to the serial implementation