AI 中文总结
本文提出多级动态稀疏化方法，将拟阵秘书问题的单一参考集扩展为嵌套层级，实现任意拟阵上的 $(e+\eps)$-概率竞争算法，最坏查询复杂度 $O_\eps(n^2)$。
AI 中文摘要
在拟阵秘书问题中，加权元素以随机顺序到达，在线算法必须不可撤销地接受元素，使其构成高权重的独立集。动态稀疏化是近期提出的一种概念简单的 $3.1462$-竞争算法，用于拟阵秘书问题，该算法维护一个随机参考集。给定该参考集后，其最大权重独立子集中的元素以依赖于时间的概率被独立接受。我们将此方法扩展，用有限嵌套参考集层级替代单一参考集。对于任意固定的 $\eps>0$，所得算法对任意拟阵具有 $(e+\eps)$-概率竞争性，最坏情况下查询次数为 $O_\eps(n^2)$。
英文摘要
In the matroid secretary problem, weighted elements arrive in random order, and an online algorithm must irrevocably accept elements forming a high-weight independent set. Dynamic Thinning is a recent, conceptually simple $3.1462$-competitive algorithm for the matroid secretary problem that maintains a random reference set. Given this reference set, the elements in its maximum-weight independent subset have been accepted independently with a time-dependent probability. We extend this approach by replacing the single reference set with a finite hierarchy of nested reference sets. For every fixed $\eps>0$, the resulting algorithm is $(e+\eps)$-probability-competitive for arbitrary matroids, with $O_\eps(n^2)$ queries in the worst case.
