We provide a simple $(1-O(\frac{1}{\sqrt{k}}))$-selectable Online Contention Resolution Scheme for $k$-uniform matroids against a fixed-order adversary. If $A_i$ and $G_i$ denote the set of selected elements and the set of realized active elements among the first $i$ (respectively), our algorithm selects with probability $1-\frac{1}{\sqrt{k}}$ any active element $i$ such that $|A_{i-1}| + 1 \leq (1-\frac{1}{\sqrt{k}})\cdot \mathbb{E}[|G_i|]+\sqrt{k}$. This implies a $(1-O(\frac{1}{\sqrt{k}}))$ prophet inequality against fixed-order adversaries for $k$-uniform matroids that is considerably simpler than previous algorithms [Ala14, AKW14, JMZ22]. We also prove that no OCRS can be $(1-\Omega(\sqrt{\frac{\log k}{k}}))$-selectable for $k$-uniform matroids against an almighty adversary. This guarantee is matched by the (known) simple greedy algorithm that accepts every active element with probability $1-\Theta(\sqrt{\frac{\log k}{k}})$ [HKS07].

翻译：我们针对固定顺序对手的$k$-均匀拟阵，提出一种简单且满足$(1-O(\frac{1}{\sqrt{k}}))$可选择性在线竞争解决方案。设$A_i$和$G_i$分别表示前$i$个元素中已选元素集合和已实现活跃元素集合，我们的算法以概率$1-\frac{1}{\sqrt{k}}$选择满足$|A_{i-1}| + 1 \leq (1-\frac{1}{\sqrt{k}})\cdot \mathbb{E}[|G_i|]+\sqrt{k}$的任意活跃元素$i$。这推导出$k$-均匀拟阵下针对固定顺序对手的$(1-O(\frac{1}{\sqrt{k}}))$先知不等式，且算法较以往方案[Ala14, AKW14, JMZ22]更为简洁。同时证明，面对全能对手时，不存在可达到$(1-\Omega(\sqrt{\frac{\log k}{k}}))$可选择的$k$-均匀拟阵在线竞争解决方案。该保障与已知的简单贪婪算法（以概率$1-\Theta(\sqrt{\frac{\log k}{k}})$接受每个活跃元素）[HKS07]相匹配。