发表机构
University of Illinois Chicago（伊利诺伊大学芝加哥分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对IID列表更新问题，本文证明在任意初始排序下，转置规则经多项式次查询后，期望代价达到OPT+O(1)，优于先前仅保证平稳态的结果。
AI 中文摘要
在经典列表更新问题中，一组项目必须存储于列表型结构中，访问第$i$个元素的代价为$i$。项目将根据项目上的某个概率分布$p$以IID（独立同分布）方式被查询。我们旨在最小化每次查询的期望代价。最优顺序是按概率$p_1 \geq p_2 \geq \cdots$的降序排列项目，期望代价为$\mathsf{OPT} = \sum_j j p_j$，但概率向量$p$通常是未知的。因此，我们采用遵循转置规则的自组织列表：每当一个项目被查询时，它向前移动1个位置。Coester（2026）证明了，在转置规则的平稳测度下，查询的期望代价至多为$\mathsf{OPT} + 1$。然而，该马尔可夫链的混合时间可能任意慢。我们证明，对于任意$p$和任意初始排序$σ$，在项目数量的多项式次查询之后，查询的期望代价至多为$\mathsf{OPT} + O(1)$。
英文摘要
In the classical list update problem, a set of items must be stored in a list-type structure, where accessing the $i$-th element costs $i$. Items will be queried in an IID manner according to some probability distribution $p$ on the items. We want to minimize the expected cost of each query. The optimal order is to place the items in decreasing order of probability $p_1 \geq p_2 \geq \cdots$ with expected cost $\mathsf{OPT} = \sum_j j p_j$, but the probability vector $p$ is generally unknown. Thus we use a self-organizing list following the transposition rule: an item is transposed 1 position forward whenever it is queried. Coester (2026) proved that, at stationarity measure for the transposition rule, the expected cost of a query is at most $\mathsf{OPT} + 1$. However, this Markov chain may have arbitrarily slow mixing time. We prove that, for arbitrary $p$ and arbitrary initial orderings $σ$, after polynomially many queries in the number of items, the expected cost of a query is at most $\mathsf{OPT} + O(1)$.
Comments11 pages
