AI 中文总结
该研究针对简单链结构的在线区间选择问题，在随机顺序模型下分析了无记忆单向撤销算法的竞争比，并与无撤销贪心算法、对抗模型下的撤销算法对比，同时得到了建议复杂度的下界。
AI 中文摘要
区间集合$I = \{ I_1, I_2, \dots, I_n \}$若满足对每个$2 \leq i \leq n-1$，区间$I_i$仅与$I_{i-1}$和$I_{i+1}$重叠，则构成一条简单链。我们证明，在随机顺序模型下，一种无记忆的单向撤销确定性算法在该简单链上的竞争比为$2(1 - 1/\sqrt{e}) \approx 0.786$；该算法的表现差于无撤销的基础贪心算法（其竞争比为$(1 - 1/e^2) \approx 0.864$），但优于对抗模型中任何确定性撤销算法（其竞争比至多为0.75）。对抗模型下的证明还给出了建议复杂度的下界$n/4$。
英文摘要
A set of intervals $I = \{ I_1, I_2, \dots, I_n \}$ forms a simple chain if, for every $2\leq i \leq n-1$, interval $I_i$ overlaps only with $I_{i-1}$ and $I_{i+1}$. We show that a deterministic memoryless one-directional revoking algorithm achieves a competitive ratio of $2(1 - 1/\sqrt{e}) \approx 0.786$ on the simple chain in the random order model, hence performs worse than the basic greedy algorithm without revoking that has a competitive ratio of $(1 - 1/e^2) \approx 0.864$, but better than any deterministic revoking algorithm in the adversarial model that has a competitive ratio of at most $0.75$. The proof of the latter also leads to a lower bound of $n/4$ for the advice complexity.
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