发表机构
University of California, Irvine; Texas A&M University（加州大学尔湾分校; 德克萨斯农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对图上的子模福利最大化与路由耦合问题，证明固定路由下目标仍具子模性，提出WHIRL算法交替优化路由与分配，具有有限收敛保证和显式近似界，数值实验验证了其质量与成本的权衡。
AI 中文摘要
本文研究图上的联合子模福利最大化与路由问题，其中智能体在收益递减条件下选择物品，并通过具有拥塞依赖成本的网络进行运输。尽管福利最大化允许基于拟阵的近似，且路由在模成本下可简化为最短路径问题，但两者的耦合产生了超模交互，破坏了可分离性。我们证明，对于固定路由，目标函数在分配变量上仍保持子模性，从而实现有原则的分解。基于此性质，我们提出了基于福利的层次路由算法（WHIRL），该算法在易处理的路由更新与分配更新之间交替进行。路由通过其模对应部分初始化，而超模效应则被建模为有界扰动。该方法具有有限收敛保证，且近似界明确依赖于与模路由的偏差。数值结果展示了路由诱导耦合的影响，并表明WHIRL在解质量与计算成本之间实现了有利的权衡。
英文摘要
This paper studies joint submodular welfare maximization and routing over graphs, where agents select items under diminishing returns and transport them through a network with congestion-dependent costs. Although welfare maximization admits matroid-based approximations and routing reduces to shortest paths under modular costs, their coupling creates supermodular interactions that break separability. We show that, for fixed routing, the objective remains submodular in the allocation variable, enabling a principled decomposition. Building on this property, we propose the Welfare-based Hierarchical Routing Algorithm (WHIRL), which alternates between tractable routing and allocation updates. Routing is initialized through its modular counterpart, while supermodular effects are modeled as bounded perturbations. The method has finite convergence guarantees and approximation bounds that depend explicitly on the deviation from modular routing. Numerical results illustrate the impact of routing-induced coupling and show that WHIRL achieves a favorable tradeoff between solution quality and computational cost.
