A dataset for suggesting variable orderings for cylindrical algebraic decompositions

This dataset contains the running time and the number of cells of the CylindricalAlgebraicDecompose command in the RegularChains library of Maple under all possible variable orderings for more than 20K number of randomly generated polynomial systems of three variables (12141 examples) and four variables (11800 examples). For each example, the running time of the worst ordering is at least twice that of the best variable ordering. It can be used for benchmarking and designing heuristic methods and machine learning models for suggesting variable orderings for CADs. Please refer readme.txt for more detailed information of the dataset and the tiny difference between v1, v2 and v3.

搜集汇总

背景与挑战

背景概述

该数据集专为圆柱代数分解（CAD）的变量顺序建议而设计，包含超过20K个随机生成的三变量和四变量多项式系统，记录了所有可能变量顺序下的运行时间和单元数量，其中每个示例的最差顺序运行时间至少是最佳顺序的两倍，凸显了变量顺序对CAD性能的关键影响。数据集适用于基准测试和开发启发式方法或机器学习模型，以优化CAD的变量选择策略。