A comparison of three heuristics to choose the variable ordering for CAD
Zongyan Huang, Matthew England, David Wilson, James H. Davenport and, Lawrence C. Paulson
TL;DR
This paper compares three heuristics for selecting variable orderings in cylindrical algebraic decomposition (CAD), demonstrating how the choice impacts problem feasibility and complexity across thousands of examples.
Contribution
It provides an empirical comparison of three heuristics for variable ordering in CAD, highlighting their effectiveness on a large dataset.
Findings
Different heuristics perform variably depending on problem instances.
The choice of variable ordering significantly affects CAD feasibility.
Some heuristics outperform others in specific problem categories.
Abstract
Cylindrical algebraic decomposition (CAD) is a key tool for problems in real algebraic geometry and beyond. When using CAD there is often a choice over the variable ordering to use, with some problems infeasible in one ordering but simple in another. Here we discuss a recent experiment comparing three heuristics for making this choice on thousands of examples.
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