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} {\alpha} {\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 - {\alpha}, 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 {\alpha} increases. These are complemented with (often tight) lower bounds on the competitive ratio of online algorithms with RIA for the three problems.
翻译:我们引入了一种对在线算法进行严格定量评估的新方法,该方法放松了经典竞争性分析的“激进最坏情况”视角。 与先前的工作相比,我们的方法,即随机灌输的建议(RIA),并不对输入序列作任何概率假设,也不依赖开发指定的在线算法。相反,它可以适用于现有的在线随机算法,引入一种手段来评估其处于极端最坏情况制度之外的情形中的性能。更具体地说,一个具有“最坏情况”视角的“最坏情况”在线算法,它从全然但并不完全可靠或极不可靠的建议中产生一些好处。新方法的关键在于将建议写入ALG的缓冲 B,而ALG通常从中读出随机部分,从而使我们能够通过非常简单和非侵入性的界面来增加它。 (Oright) 的可靠性通过一个参数来捕捉到。 (liveral ) ALG 和 liver (perround) 的 Rial 比率, 由在线的 orral dreal 来决定, 的概率, 如果 直为在线 的 直系, 直径 直径,, 直系 直系 直系, 直系 直系 直系 直系 直系, 直系 直系 直系 直系 直系 直系 直系 直系 直系, 直系 直系 直系 直系 直系 直系, 直系 直系 直系 直系 直系 直系, 直系 直系 直系 直系 直系 直系 直系 直系, 直系 直系 直系 直系 直系 直系 直系 直系 直系 直系 。