Whereas there are simple algorithms that are proven to be optimal for the Classical and the Multiple Choice Secretary Problem, the Matroid Secretary Problem is less thoroughly understood. This paper proposes the generalization of some simple algorithms from the Classical and Multiple Choice versions on the Matroid Secretary Problem. Out of two algorithms that make decisions based on samples, like the Dynkin's algorithm, one is proven to be an instance of Greedy Algorithm (Bahrani et al., 2022), while the other is not. A generalized version of the Virtual Algorithm (Babaioff et al., 2018) obtains a constant competitive ratio for the Hat Graph, the adversarial example for Greedy Algorithms, but fails to do so when a slight modificiation is introduced to the graph. We show that there is no algorithm with Strong Forbidden Sets (Soto et al., 2021) of size 1 on all graphic matroids.

翻译：虽然对古典和多选择秘书问题来说,简单算法被证明是最佳的,但是对马甲板秘书问题的理解却不够透彻。本文件建议对马甲板秘书问题的古典和多选择版本的某些简单算法进行概括化。在根据样本作出决定的两个算法中,例如Dynkin的算法,一个被证明是Greedy Algorithm的例子(Bahrani等人,2022年),而另一个则不是。虚拟Algorithm(Babaioff等人,2018年)的通用版本(Babaioff等人,2018年)获得一个恒星图(Ghat Gratedy Algorithms的对抗性与多重选择版本)的不变的竞争比率,但当图中引入微微调时却未能这样做。我们显示,在所有图形型甲状腺上没有1号的“强受禁装置”(Soto等人,2021年)的算法。