基于SAT求解器计算非负秩的下界
Computing Lower Bounds on the Non-negative Rank via SAT Solvers
浏览论文内容
中文总结 AI 辅助
该研究针对矩形及改进的矩形覆盖提出公式，结合SAT求解器改进了多个非负矩阵的非负秩下界，还确定了部分正多边形的扩展复杂度。
中文摘要 AI 辅助
求多面体的扩展复杂度（xc）等价于求其松弛矩阵的非负秩。我们针对矩形及改进的矩形覆盖提出一种公式，用于界定各类非负矩阵的非负秩。尽管已有相关下界，但我们的公式可让我们使用布尔可满足性（SAT）求解器，该工具被证明十分有效。我们得到了多个矩阵非负秩下界的改进值，尤其确定了一些正多边形的xc。
英文摘要
Finding the extension complexity (xc) of a polytope is equivalent to finding the non-negative rank of its slack matrix. We provide a formulation for the rectangle and refined rectangle covering, bounding the non-negative rank of diverse non-negative matrices. While the bounds are known, our formulation enables us to use boolean satisfiability (SAT) solvers, which proves to be a strong tool. We obtain improved values for lower bounds on the non-negative rank of multiple matrices. In particular, we determined the xc of some regular polygons.
