基于组合二分法的加权k-服务器界
Weighted k-Server Bounds via Combinatorial Dichotomies
摘要：
加权$k$ -服务器问题是$k$ -服务器问题的自然推广，其中每个服务器具有不同的权重。我们考虑统一度量的问题，这对应于分页的自然推广。我们的主要结果是一个双指数的竞争比的任何确定性的在线算法的下限，基本上匹配已知的上限的问题，并关闭一个大的和长期存在的差距。该下界是基于将加权$k$ -服务器问题与某个组合问题联系起来，并证明了该组合问题的一个Ramsey理论下界，这种组合联系还揭示了服务于一系列请求的低成本可行解的若干结构性质.我们用它来表明，广义功函数算法实现了几乎最佳的竞争比，并获得新的细化的竞争比的情况下，$d$不同的权重类的上界。
英文摘要：
The weighted $k$-server problem is a natural generalization of the $k$-server problem where each server has a different weight. We consider the problem on uniform metrics, which corresponds to a natural generalization of paging. Our main result is a doubly exponential lower bound on the competitive ratio of any deterministic online algorithm, that essentially matches the known upper bounds for the problem and closes a large and long-standing gap. The lower bound is based on relating the weighted $k$-server problem to a certain combinatorial problem and proving a Ramsey-theoretic lower bound for it. This combinatorial connection also reveals several structural properties of low cost feasible solutions to serve a sequence of requests. We use this to show that the generalized Work Function Algorithm achieves an almost optimum competitive ratio, and to obtain new refined upper bounds on the competitive ratio for the case of $d$ different weight classes.
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。
