独立系统的拟阵逼近
Matroidal Approximations of Independence Systems
摘要：
Milgrom（2017）提出了一种启发式方法，用于确定独立系统${\mathcal I}$的最大权重基，因为我们只需要对指定的${\mathcal O}\subseteq {\mathcal I}$中的集合进行近似保证。该${\mathcal O}$反映了设计者关于最佳基的位置的先验知识。启发式是基于找到一个“内部拟阵”，一个包含在独立系统。我们表明，即使在${\mathcal O}={\mathcal I}$的零附加知识的情况下，这种新的启发式的最坏情况下的性能可以优于经典的贪心算法。
英文摘要：
Milgrom (2017) has proposed a heuristic for determining a maximum weight basis of an independence system ${\mathcal I}$ given that we want an approximation guarantee only for sets in a prescribed ${\mathcal O}\subseteq {\mathcal I}$. This ${\mathcal O}$ reflects prior knowledge of the designer about the location of the optimal basis. The heuristic is based on finding an `inner matroid', one contained in the independence system. We show that even in the case ${\mathcal O}={\mathcal I}$ of zero additional knowledge the worst-case performance of this new heuristic can be better than that of the classical greedy algorithm.
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。
