发表机构
Duke University; Google Research; Rutgers University; Technion – Israel Institute of Technology（杜克大学; 谷歌研究; 罗格斯大学; 以色列理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文研究带样本的在线算法（OAS），提出紧竞争比算法，改进集合覆盖等问题的界，并引入对抗鲁棒变体，获得多个问题的紧界。
AI 中文摘要
假设一个在线算法被给予其输入的一个无偏 $p$-样本作为离线建议；该算法能否利用该样本实现超越最坏情况的性能？我们研究带样本的在线算法（OAS）模型。我们为集合覆盖问题展示了一个紧的 $O\left(\log (1/p) \cdot \log m + \log n\right)$-竞争算法，指数级地改进了 Gupta 等人（SODA'24）的 $O\left(1/p \cdot \log (mn)\right)$ 保证，并回答了其中的一个开放问题。我们的技术扩展到覆盖整数规划和非度量设施选址问题，也为这些问题产生了紧界。进一步，我们为度量设施选址问题给出了一个 $O(\log (1/p)/ \log \log (1/p))$-竞争算法，回答了 Argue 等人（NeurIPS'22）的一个开放问题。然后我们引入并研究了 OAS 模型的鲁棒变体，在该变体中，对手被允许任意修改 $p$-样本中的 $k$ 个元素。对于集合覆盖、覆盖整数规划和非度量设施选址，我们获得了紧竞争比 $O\left(\log (k/p) \cdot \log m + \log n\right)$。对于度量设施选址和 Steiner 树，我们分别获得了紧竞争比 $O\left(\log (k/p) / \log \log (k/p) \right)$ 和 $O\left(\log (k/p)\right)$。据我们所知，这些是 OAS 设置中鲁棒算法的首批结果。
英文摘要
Suppose an online algorithm is given an unbiased $p$-sample of its input as offline advice; can the algorithm exploit the sample to achieve beyond-worst-case performance? We study this online algorithms with a sample (OAS) model. We show a tight $O\left(\log (1/p) \cdot \log m + \log n\right)$-competitive algorithm for set cover, exponentially improving upon the $O\left(1/p \cdot \log (mn)\right)$ guarantee of Gupta et al. (SODA'24) and answering an open question therein. Our techniques extend to covering integer programs and non-metric facility location, also yielding tight bounds for these problems. Further, we give an $O(\log (1/p)/ \log \log (1/p))$-competitive algorithm for metric facility location, answering an open question of Argue et al. (NeurIPS'22). We then introduce and study the robust variant of the OAS model, in which an adversary is allowed to arbitrarily modify $k$ elements of the $p$-sample. For set cover, covering integer programs, and non-metric facility location, we obtain a tight competitive ratio of $O\left(\log (k/p) \cdot \log m + \log n\right)$. For metric facility location and Steiner tree, we obtain tight competitive ratios of $O\left(\log (k/p) / \log \log (k/p) \right)$ and $O\left(\log (k/p)\right)$ respectively. To the best of our knowledge, these are the first results for robust algorithms in the OAS setting.
