测试完全对偶完整性的替代方法
Alternatives for Testing Total Dual Integrality
摘要：
在本文中，我们提供了TDI系统的特征性质，其中包括以下内容：一个系统的线性不等式是TDI当且仅当其系数向量形成一个希尔伯特基，并存在一个测试集的系统的对偶整数规划，其中所有的测试向量有正项等于1。重新这提供了计算代数和整数规划之间的关系，他们包含Applegate，库克和麦考密克的充分条件的TDI财产和Sturmfels'定理有关复曲面初始理想所产生的平方自由单项式单模三角。我们还研究了这里提出的TDI属性的表征的理论和实践效率和限制。在集合填充多面体的特殊情况下，我们的结果对应于赋予弱完美图定理一个额外的、计算上有趣的几何功能：完美图的独立集多面体的法向扇可以精化为仅由幺模锥组成的正则三角剖分。
英文摘要：
In this paper we provide characterizing properties of TDI systems, among others the following: a system of linear inequalities is TDI if and only if its coefficient vectors form a Hilbert basis, and there exists a test-set for the system's dual integer programs where all test vectors have positive entries equal to 1. Reformulations of this provide relations between computational algebra and integer programming and they contain Applegate, Cook and McCormick's sufficient condition for the TDI property and Sturmfels' theorem relating toric initial ideals generated by square-free monomials to unimodular triangulations. We also study the theoretical and practical efficiency and limits of the characterizations of the TDI property presented here. In the particular case of set packing polyhedra our results correspond to endowing the weak perfect graph theorem with an additional, computationally interesting, geometric feature: the normal fan of the stable set polytope of a perfect graph can be refined into a regular triangulation consisting only of unimodular cones.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
