基于标记法的带储备高效缓存
Efficient Caching with Reserves via Marking
AI总结：
本文提出结合势函数上界与对偶拟合下界的新分析技术，应用于带储备缓存问题得到O(log k)竞争比的分数及随机整数在线算法，并为经典无权重分页随机标记法给出新证明。
摘要：
在线缓存是在线算法领域最基础且研究最充分的问题之一。包括势函数和原始对偶技术在内的创新算法思想与分析方法，为这一仍在发展的领域提供了深刻洞见。本文提出一种新的分析技术：首先使用势函数给出在线算法的成本上界，再结合一种新的对偶拟合策略给出离线最优算法的成本下界。我们将这些技术应用于Ibrahimpur等人[10]近期提出的带储备缓存（Caching with Reserves）问题，通过标记策略得到了竞争比为O(log k)的分数型在线算法，其中k表示缓存大小。我们还设计了一种新的多项式时间在线舍入算法，以得到竞争比为O(log k)的随机化整数算法。此外，我们为经典无权重分页问题的随机标记法提供了一种全新的简洁证明。
英文摘要：
Online caching is among the most fundamental and well-studied problems in the area of online algorithms. Innovative algorithmic ideas and analysis -- including potential functions and primal-dual techniques -- give insight into this still-growing area. Here, we introduce a new analysis technique that first uses a potential function to upper bound the cost of an online algorithm and then pairs that with a new dual-fitting strategy to lower bound the cost of an offline optimal algorithm. We apply these techniques to the Caching with Reserves problem recently introduced by Ibrahimpur et al. [10] and give an O(log k)-competitive fractional online algorithm via a marking strategy, where k denotes the size of the cache. We also design a new online rounding algorithm that runs in polynomial time to obtain an O(log k)-competitive randomized integral algorithm. Additionally, we provide a new, simple proof for randomized marking for the classical unweighted paging problem.
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