随机顺序在线设施选址中到达时间的作用
The Power of Arrival Times in Random-Order Online Facility Location
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中文总结 AI 辅助
研究随机顺序模型下在线度量设施选址问题，给出两种改进算法，确定性算法竞争比低于2.42，随机算法竞争比低于2.59且在对抗模型中保留渐近最优比，关键是决策时考虑请求到达时间利用其携带的局部密度信息。
中文摘要 AI 辅助
我们研究随机顺序模型（Meyerson FOCS'01）中具有统一开放成本的在线度量设施选址问题。此前最好的上限是一个3竞争比的随机算法（Kaplan、Naori、Raz SODA'23），与已知最佳下限2之间存在差距。在这项工作中，我们给出了两种具有改进竞争比的算法：（i）一种竞争比低于2.42的确定性算法；（ii）一种竞争比低于2.59的随机算法，且在对抗顺序模型中保留渐近最优的O(log n/log log n)竞争比。关键改进是在做出开放决策时考虑请求的到达时间：到达时间携带请求周围局部密度的几何信息，这从根本上帮助了算法。
英文摘要
We study online metric facility location with uniform opening costs in the random-order model (Meyerson FOCS'01). The best previous upper bound was a $3$-competitive randomized algorithm (Kaplan, Naori, Raz SODA'23), leaving a gap to the best known lower bound of $2$. In this work, we give two algorithms with improved competitive ratios: (i) a deterministic algorithm with a competitive ratio below $2.42$ and (ii) a randomized algorithm with a competitive ratio below $2.59$ and the additional property that it retains the asymptotically optimal $O(\log n/\log \log n)$ competitive ratio in the adversarial-order model. A key improvement is to take the arrival time of the request into consideration when making opening decisions: The arrival time carries geometric information about the local density around the request, which fundamentally helps the algorithm.
