It is well known that the variable ordering can be critical to the efficiency or even tractability of the cylindrical algebraic decomposition (CAD) algorithm. We propose new heuristics inspired by complexity analysis of CAD to choose the variable ordering. These heuristics are evaluated against existing heuristics with experiments on the SMT-LIB benchmarks using both existing performance metrics and a new metric we propose for the problem at hand. The best of these new heuristics chooses orderings that lead to timings on average 17% slower than the virtual-best: an improvement compared to the prior state-of-the-art which achieved timings 25% slower.

翻译：众所周知,变量定序对于圆柱形代数分解算法( CAD) 的效率甚至可移动性至关重要。 我们提出基于对 CAD 复杂分析的新的超自然学来选择变量顺序。 这些超自然学用SMT-LIB 基准的实验用SMT-LIB 基准来评估现有的超自然学。 这些新超自然学的最好选择的定序平均比虚拟最佳的定序慢17%:比先前的时速慢25%的时速要好。