发表机构
IIIT Delhi; North Carolina State University（德里信息技术研究所; 北卡罗来纳州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出鲁棒化贪心算法解决在线运输问题，改进竞争比至6.6604k-2.89，保留度量敏感保证，并证明最近邻分配占成本近半，实验验证其优越性。
AI 中文摘要
我们研究在线运输问题，在该问题中，度量空间中依次到达的 n 个请求必须被不可撤销地分配给 k 个有容量的设施。除了经典的物流应用外，该问题还模拟了机器学习中出现的资源分配任务，包括在线设施分配、推荐系统和专家混合路由。我们引入了鲁棒化贪心（RG）算法，这是鲁棒匹配算法的一种确定性推广，其竞争比为 6.6604k-2.89，改进了现有最优边界 8k-7（Arndt 等人，SOSA 2026）和 8k-5（Harada 和 Itoh，ICALP 2025）。RG 还保留了为鲁棒匹配（RM）算法（Nayyar 和 Raghvendra，FOCS 2017）建立的度量敏感保证，在固定 d>1 的 d 维欧几里得空间中实现了 O(k^{1-1/d}\log^2 n) 的竞争比。对于 Arndt 等人或 Harada 和 Itoh 的运输算法，没有已知的类似度量敏感保证。除了这些竞争保证之外，RG 为其决策提供了简单的解释。它倾向于自然的最近邻分配，并且对于合适的参数，仅当它识别出能够降低其维护的辅助匹配成本的重新分配时，才偏离此选择，从而纠正累积的分配成本。我们还证明了，即使在对抗性到达情况下，最近邻分配也占 RG 总成本的保证比例，对于适当参数接近二分之一。在真实数据集上的实验证实了该理论：RG 实现了比竞争算法更低的成本与最优值之比，同时在其成本中保留了大量的最近邻成分。
英文摘要
We study the \emph{online transportation problem}, in which $n$ requests arriving sequentially in a metric space must be irrevocably assigned to $k$ capacitated facilities. Beyond classical logistics applications, this problem models resource-allocation tasks arising in machine learning, including online facility assignments, recommender systems, and mixture-of-experts routing. We introduce \emph{Robustified Greedy} (RG), a deterministic generalization of the Robust Matching algorithm that achieves a competitive ratio of $6.6604k-2.89$, improving upon the state-of-the-art bounds of $8k-7$ (Arndt et al., SOSA 2026) and $8k-5$ (Harada and Itoh, ICALP 2025). RG also retains the metric-sensitive guarantee established for Robust Matching (RM) (Nayyar and Raghvendra, FOCS 2017), achieving a competitive ratio of $O(k^{1-1/d}\log^2 n)$ in $d$-dimensional Euclidean spaces for fixed $d>1$. No comparable metric-sensitive guarantee is known for the transportation algorithms of Arndt et al.\ or Harada and Itoh. Beyond these competitive guarantees, RG provides a simple explanation for its decisions. It favors the natural nearest-neighbor assignment and, for suitable parameters, departs from this choice only when it identifies a reassignment that reduces the cost of its maintained auxiliary matching, thereby correcting accumulated assignment costs. We also prove that nearest-neighbor assignments account for a guaranteed fraction of RG's total cost, approaching one-half for appropriate parameters, even under adversarial arrivals. Experiments on real-world datasets corroborate the theory: RG achieves lower cost-to-\textsc{Opt} ratios than the competing algorithms while retaining a substantial nearest-neighbor component in its cost.
