通过贪心方法改进不可分割CVRP的近似算法
Improved Approximation for Unsplittable CVRP via a Greedy Approach
浏览论文内容
中文总结 AI 辅助
针对不可分割容量约束车辆路径问题，提出平均贪心算法，结合行程划分与匹配，实现多项式时间3.159-近似。
中文摘要 AI 辅助
我们为度量不可分割容量约束车辆路径问题设计了一种多项式时间的$3.159$-近似算法。我们基于Traub（2025）提出的相对贪心算法，该算法可视为Friggstad、Mousavi、Rahgoshay和Salavatipour（2025）的LP舍入算法的一种变体。我们的主要创新是平均贪心算法，这是一种新算法，能够同时控制行程成本和高需求客户的覆盖范围。这种额外的控制使得后续贪心选择的成本能够采用更精细的平均论证。与Zhao和Xiao（2026）类似，将平均贪心算法与行程划分变体及匹配算法相结合，最终得到近似保证。
英文摘要
We devise a polynomial-time $3.159$-approximation algorithm for the metric unsplittable Capacitated Vehicle Routing Problem. We build on the Relative Greedy Algorithm suggested by Traub (2025), which can be considered as a variant of the LP rounding algorithm of Friggstad, Mousavi, Rahgoshay, and Salavatipour (2025). Our main ingredient is the Average Greedy Algorithm, a new algorithm that controls both tour costs and the coverage of clients with high demand. This additional control enables a sharper averaging argument for the cost of subsequent greedy choices. Similarly to Zhao and Xiao (2026), combining the Average Greedy with variants of tour partitioning and a matching algorithm yields the final approximation guarantee.
发表机构
- Research Institute for Discrete Mathematics, Bonn, Germany（波恩离散数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
