On the Parallelization of Triangular Decomposition of Polynomial Systems
Abstract
We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on polynomials and high-level procedures which produce the different components (points, curves, surfaces) of the solution set. The latter "component-level" parallelization of triangular decompositions, our focus here, belongs to the class of dynamic irregular parallel applications. Possible speedup factors depend on geometrical properties of the solution set (number of components, their dimensions and degrees); these algorithms do not scale with the number of processors. In this paper we combine two different concurrency schemes, the fork-join model and producer-consumer patterns, to better capture opportunities for component-level parallelization. We report on our implementation with the publicly available BPAS library. Our experimentation with 340 systems yields promising results.
Cite
@article{arxiv.1906.00039,
title = {On the Parallelization of Triangular Decomposition of Polynomial Systems},
author = {Mohammadali Asadi and Alexander Brandt and Robert H. C. Moir and Marc Moreno Maza and Yuzhen Xie},
journal= {arXiv preprint arXiv:1906.00039},
year = {2019}
}