We show that a simple greedy algorithm is $4.75$ probability-competitive for the Laminar Matroid Secretary Problem, improving the $3\sqrt{3} \approx 5.17$-competitive algorithm based on the forbidden sets technique (Soto, Turkieltaub, and Verdugo, 2018).

翻译：我们证明，一个简单的贪婪算法在层状拟阵秘书问题中具有$4.75$的概率竞争力，改进了基于禁止集技术的$3\sqrt{3} \approx 5.17$竞争力算法（Soto, Turkieltaub, and Verdugo, 2018）。