发表机构
School of Mathematics Science, Ocean University of China（中国海洋大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究带截止时间的在线线路聚合问题，提出最优e-竞争随机算法及学习增强算法，在鲁棒性与一致性间取得权衡，并给出离线动态规划解法。
AI 中文摘要
我们研究带截止时间的在线线路聚合问题，其中请求随时间到达正半轴上，位于位置$y$的服务会以成本$y$清除$[0,y]$中的所有待处理请求。在经典对抗设置中，我们提出一个针对不知情对手的$e$-竞争随机算法，并证明匹配的下界。因此$e$是最优随机竞争比。随后我们考虑以离线可行解形式给出的建议。对于每个置信参数$\lambda\in(0,1]$，我们的确定性学习增强算法具有$(1+3/\lambda)$-鲁棒性和$(1+3\lambda)$-一致性。我们还提出一个随机学习增强算法，针对不知情对手具有$(e+e/\lambda)$-鲁棒性和$(e-1+\lambda)$-一致性。对于离线问题，我们提出一个多项式时间动态规划算法。数值实验补充了最坏情况分析：准确的建议降低服务成本，而两种学习增强算法在建议变得日益嘈杂时仍保持稳定。
英文摘要
We study online line aggregation with deadlines, where requests arrive over time on the positive half-line and a service at location $y$ clears all pending requests in $[0,y]$ at cost $y$. In the classical adversarial setting, we propose an $e$-competitive randomized algorithm against an oblivious adversary and prove a matching lower bound. Thus $e$ is the optimal randomized competitive ratio. We then consider advice in the form of an offline feasible solution. For every confidence parameter $λ\in(0,1]$, our deterministic learning-augmented algorithm is $(1+3/λ)$-robust and $(1+3λ)$-consistent. We also propose a randomized learning-augmented algorithm that is $(e+e/λ)$-robust and $(e-1+λ)$-consistent against an oblivious adversary. For the offline problem, we present a polynomial-time dynamic programming algorithm. Numerical experiments complement the worst-case analysis: accurate advice lowers service costs, while both learning-augmented algorithms remain stable as the advice becomes increasingly noisy.
