AI 中文总结
针对带任意延迟函数的多级聚合问题，提出新在线算法，通过双拟合框架将竞争比优化为2D，缩小了与截止日期变体的渐近差距。
AI 中文摘要
针对带有任意延迟函数的著名多级聚合问题（MLAP），我们提出一种新的在线算法，实现了2D的竞争比，其中D是基础树的深度。该结果改进了当前已知的最佳竞争比O(D²)，并渐近匹配了此前仅在截止日期变体中已知的D竞争比边界，从而缩小了两种设置之间的渐近差距。我们的核心技术贡献是一种新颖的双拟合框架，可为两种设置提供统一分析；特别地，该框架还为带截止日期的MLAP确立了D竞争比。我们的分析基于两个新思想：一是事后双构造，解决了传统在线原-对偶方法中的不可行性问题；二是依赖时间的双打包，可在动态请求集上保持可行性。
英文摘要
We present a new online algorithm for the well-known Multi-Level Aggregation Problem (MLAP) with arbitrary delay functions, achieving a $2D$-competitive ratio, where $D$ is the depth of the underlying tree. This result improves the current best-known competitive ratio of $O(D^2)$ and asymptotically matches the $D$-competitive bound previously known only for the deadline variant, thereby closing the asymptotic gap between the two settings. Our key technical contribution is a novel dual fitting framework that provides a unified analysis for both settings; in particular, it also establishes a $D$-competitive ratio for MLAP with deadlines. Our analysis is built upon two new ideas: a hindsight dual construction, which resolves the infeasibility issues in traditional online primal-dual methods, and a time-dependent dual packing that maintains feasibility over dynamic request sets.
