Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition

TL;DR

This paper employs machine learning, specifically support vector machines, to select optimal variable orderings in cylindrical algebraic decomposition, significantly improving heuristic choices and computational feasibility in algebraic geometry tasks.

Contribution

It introduces a machine learning approach to automatically choose the best heuristic for variable ordering in CAD, outperforming individual heuristics.

Findings

Support vector machine effectively predicts the best heuristic.

Machine learning improves CAD performance over traditional heuristics.

Enhanced feasibility of algebraic geometry computations.

Abstract

Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables. This can be important, with some problems infeasible with one variable ordering but easy with another. Machine learning is the process of fitting a computer model to a complex function based on properties learned from measured data. In this paper we use machine learning (specifically a support vector machine) to select between heuristics for choosing a variable ordering, outperforming each of the separate heuristics.