The Spark Randomizer: a learned randomized framework for computing Gr\"obner bases
Commutative Algebra
2023-06-16 v1
Abstract
We define a violator operator which captures the definition of a minimal Gr\"obner basis of an ideal. This construction places the problem of computing a Gr\"obner basis within the framework of violator spaces, introduced in 2008 by G{\"a}rtner, Matou{\v{s}}ek, R{\"u}st, and {\v{S}}kovro{\v{n}} in a different context. The key aspect which we use is their successful utilization of a Clarkson-style fast sampling algorithm from geometric optimization. Using the output of a machine learning algorithm, we combine the prediction of the size of a minimal Gr\"obner basis of an ideal with the Clarkson-style biased random sampling method to compute a Gr\"obner basis in expected runtime linear in the size of the violator space.
Cite
@article{arxiv.2306.08279,
title = {The Spark Randomizer: a learned randomized framework for computing Gr\"obner bases},
author = {Shahrzad Jamshidi and Sonja Petrović},
journal= {arXiv preprint arXiv:2306.08279},
year = {2023}
}