具有随机注入建议的在线算法
Online Algorithms with Randomly Infused Advice
AI总结：
本文提出随机注入建议（RIA）方法，用于评估在线算法性能，不依赖传统最坏情况分析，通过引入可靠但不完全可信的预言机来改进算法在非极端最坏情况下的表现。
摘要：
我们介绍了一种新颖的方法，用于严格定量评估在线算法，该方法放松了经典竞争分析中“极端最坏情况”的视角。与先前工作不同，我们的方法（称为随机注入建议 RIA）不假设输入序列的任何概率特性，也不依赖特定的在线算法。相反，它可以应用于现有的在线随机算法，引入了一种评估其在非极端最坏情况下的性能的手段。更具体地说，具有 RIA 的在线算法 ALG 从一个全知但不完全可靠的预言机处获得建议。该方法的核心是将建议写入缓冲区 B，从其中 ALG 通常读取随机位，从而通过非常简单且非侵入性的接口来增强其性能。预言机的可靠性和不可靠性通过参数 0 ≤ α ≤ 1 来捕捉，该参数决定了每轮建议被成功注入的概率；如果建议未被注入（发生在概率 1 - α 时），则缓冲区 B 包含新的随机位（如经典在线设置）。新 RIA 方法的适用性通过将其应用于三个广泛研究的在线问题：页面置换、均匀度量任务系统和在线集合覆盖问题来展示。对于这些问题，我们建立了经典在线算法竞争比的新上界，随着注入参数 α 的增加而改进。这些结果与针对这三个问题的具有 RIA 的在线算法的竞争比的下界（通常很紧）相补充。
英文摘要：
We introduce a novel method for the rigorous quantitative evaluation of online algorithms that relaxes the "radical worst-case" perspective of classic competitive analysis. In contrast to prior work, our method, referred to as randomly infused advice (RIA), does not make any probabilistic assumptions about the input sequence and does not rely on the development of designated online algorithms. Rather, it can be applied to existing online randomized algorithms, introducing a means to evaluate their performance in scenarios that lie outside the radical worst-case regime. More concretely, an online algorithm ALG with RIA benefits from pieces of advice generated by an omniscient but not entirely reliable oracle. The crux of the new method is that the advice is provided to ALG by writing it into the buffer B from which ALG normally reads its random bits, hence allowing us to augment it through a very simple and non-intrusive interface. The (un)reliability of the oracle is captured via a parameter 0 {\le} α {\le} 1 that determines the probability (per round) that the advice is successfully infused by the oracle; if the advice is not infused, which occurs with probability 1 - α, then the buffer B contains fresh random bits (as in the classic online setting). The applicability of the new RIA method is demonstrated by applying it to three extensively studied online problems: paging, uniform metrical task systems, and online set cover. For these problems, we establish new upper bounds on the competitive ratio of classic online algorithms that improve as the infusion parameter α increases. These are complemented with (often tight) lower bounds on the competitive ratio of online algorithms with RIA for the three problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
