发表机构
Southern University of Science and Technology（南方科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文研究有限根树的在线多级聚合问题，提出DP-Envelope算法，其确定性竞争比为2、随机竞争比为e/(e-1)，均为最优且可扩展到特定静态服务系统。
AI 中文摘要
我们研究有限根树上的在线多级聚合问题，目标是每批次最大延迟。服务方为根子树以及该服务处理的请求中最大等待时间付费。我们证明离线最优解具有连续到达块的标准形式，可通过多项式时间动态规划计算。该动态规划定义了一类在线算法的截止时间，我们称之为DP-Envelope。其确定性端点具有2的竞争比；采用密度为e^θ/(e-1)的单个全局参数采样，得到对抗无知对手的e/(e-1)竞争比随机算法。确定性保证匹配已知的固定节点下界，我们还证明了匹配的随机下界，因此两种保证在所有非退化根树上均为最优。我们首先将直线度量作为热身，此时算法及其嵌套块划分具有直接几何解释。最后，我们证明上界可扩展到所有具有归一化非递减次模联合服务成本的可实现静态服务系统。
英文摘要
We study online multi-level aggregation on finite rooted trees with a per-batch maximum-delay objective. A service pays for a rooted subtree and for the maximum waiting time among the requests cleared by that service. We show that the offline optimum admits a consecutive-arrival-block normal form and can be computed by a polynomial-time dynamic program. The same dynamic program defines the deadlines of a family of online algorithms, which we call DP-Envelope. Its deterministic endpoint is $2$-competitive. Sampling one global parameter with density $e^θ/(e-1)$ leads to an $e/(e-1)$-competitive randomized algorithm against an oblivious adversary. The deterministic guarantee matches the known fixed-node lower bound, and we prove a matching randomized lower bound. Thus, both guarantees are optimal on every nondegenerate rooted tree. We first develop the line metric as a warm-up, where the algorithm and its nested block partitions have a direct geometric interpretation. Finally, we show that the upper bounds extend to every realizable static service system with a normalized, nondecreasing, submodular joint service cost.
