Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition
This work addresses a specific bottleneck in computational algebraic geometry for researchers and practitioners, but it is incremental as it applies an existing machine learning method to a known problem.
The paper tackled the problem of selecting variable orderings for cylindrical algebraic decomposition (CAD) by using a support vector machine to choose between heuristics, resulting in outperformance over individual heuristics.
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.