Reducing the size and number of linear programs in a dynamic Gr\"obner basis algorithm

TL;DR

This paper introduces two methods to significantly reduce the computational cost of a dynamic Gr"obner basis algorithm by decreasing the size and number of linear programs involved.

Contribution

It presents novel techniques to lower the overhead of solving multiple linear programs in the dynamic Gr"obner basis algorithm, making it more practical.

Findings

Two methods substantially reduce linear program size and count.

The approaches improve the efficiency of the dynamic Gr"obner basis algorithm.

The techniques address a long-standing computational bottleneck.

Abstract

The dynamic algorithm to compute a Gr\"obner basis is nearly twenty years old, yet it seems to have arrived stillborn; aside from two initial publications, there have been no published followups. One reason for this may be that, at first glance, the added overhead seems to outweigh the benefit; the algorithm must solve many linear programs with many linear constraints. This paper describes two methods of reducing the cost substantially, answering the problem effectively.