树上通过镜像下降和不公平胶合的度量任务系统
Metrical task systems on trees via mirror descent and unfair gluing
摘要：
我们考虑度量任务系统的树度量，并提出了一个$O(\mathrm{depth} \times \log n)$竞争随机算法的基础上，镜像下降框架介绍了我们以前的工作上的$k$ -服务器问题。对于特殊的情况下，层次分离树（HST），我们使用镜像下降，完善标准的方法的基础上胶合不公平的测量任务系统。这产生了HST的$O(\log n)$竞争算法，从而去除了Fiat和Mendel（2003）边界中的无关$\log\log n$。结合著名的HST嵌入定理，本文还给出了每个$n$ -点度量空间的$O((\log n)^2)$ -竞争随机算法.
英文摘要：
We consider metrical task systems on tree metrics, and present an $O(\mathrm{depth} \times \log n)$-competitive randomized algorithm based on the mirror descent framework introduced in our prior work on the $k$-server problem. For the special case of hierarchically separated trees (HSTs), we use mirror descent to refine the standard approach based on gluing unfair metrical task systems. This yields an $O(\log n)$-competitive algorithm for HSTs, thus removing an extraneous $\log\log n$ in the bound of Fiat and Mendel (2003). Combined with well-known HST embedding theorems, this also gives an $O((\log n)^2)$-competitive randomized algorithm for every $n$-point metric space.
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。
