AI 中文总结
针对低连通图上的最大覆盖网络设计问题，开发利用割点分解的动态规划框架，在多数测试案例中性能优于直接求解，还可生成完整的覆盖-预算曲线。
AI 中文摘要
规划医疗保健、应急响应和学校等可及的公共服务，通常不仅需要选择开设设施的地点，还需改善连接民众与设施的网络，例如升级易受灾害区域内易受洪水影响的道路。然而，大多数选址模型将网络视为固定的，且预算为给定值。我们研究最大覆盖网络设计问题，该问题将单一预算分配于开设设施和升级薄弱环节，以最大化在目标出行距离内可到达开放设施的人口数量。该问题即使在最简单的网络上也具有难度，规划者通常需要了解覆盖范围随预算的增长情况，而非单一规划方案。我们开发了一种精确的动态规划框架，利用了真实道路网络共有的特性：低连通性，存在许多移除后会使网络断开的割点。在树结构上，该递归是自包含的：每个状态可简化为几个简单的设施选址和升级选择，无需求解器即可快速计算，运行时间可预测；对于较大的预算和出行距离，其性能优于直接求解混合整数线性规划（MILP）公式。在一般低连通网络上，该框架在割点处分解问题，并嵌入给定的MILP公式以求解生成的子问题，通过接口处的覆盖条件协调各子问题。这使我们能够将单独的公式与框架内的同一公式进行比较：在306个测试案例中，框架在超过80%的实例上的性能与直接求解相当或更优。由于该框架在单次运行中评估所有预算水平，还可免费生成完整的覆盖范围-预算曲线，而直接求解需将时间分配给各个单独的预算。
英文摘要
Planning accessible public services such as health care, emergency response, and schools often requires not only choosing where to open facilities but also improving the network that connects people to them, for example upgrading flood-prone roads in vulnerable regions. Most location models, however, take the network as fixed and the budget as given. We study the Maximum Covering Network Design Problem, in which a single budget is shared between opening facilities and upgrading weak links to maximize the population within a target travel distance of an open facility. The problem is hard even on the simplest networks, and planners usually want to see how coverage grows with the budget, not a single plan. We develop an exact dynamic-programming framework that exploits a property common to real road networks: their low connectivity, with many cut points whose removal disconnects the network. On trees, the recursion is self-contained: each state reduces to a few simple facility and upgrade choices that are fast to compute without a solver, giving predictable running times; for larger budgets and travel distances it outperforms solving the MILP formulation directly. On general low-connectivity networks, the framework decomposes the problem at the cut points and embeds a given MILP formulation to solve the resulting pieces, coordinating them through coverage conditions at the interfaces. This lets us compare a formulation on its own against the same formulation inside the framework: across 306 test cases the framework matches or outperforms direct solving on more than 80% of instances. Because it evaluates all budget levels in a single run, it also yields the full coverage-versus-budget curve at no extra cost, whereas direct solving must split its time across individual budgets.
