发表机构
University of California Irvine; Los Alamos National Laboratory（加州大学尔湾分校; 洛斯阿拉莫斯国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究物理约束下图Greedoid基上的超模最小化问题，提出基于前瞻Oracle的条件顺序贪心算法，推导出可行性代价的闭式近似界，并通过FORWARD算法验证其紧性与权衡。
AI 中文摘要
贪心算法能高效近似组合优化问题，但当可行性将组合结构与全局物理约束耦合时，其保证会减弱。我们研究在物理诱导约束下，图 Greedoid 的基上的单调非递减超模最小化问题。我们使用一个前瞻 Oracle 来建模物理信息选择，该 Oracle 识别可扩展为可行基的候选，从而得到条件顺序贪心算法。我们推导出一个闭式近似界，称为可行性的代价，它基于 Oracle 限制候选集的变异性以及对未观测元素的概率修正。作为案例研究，我们证明 FORWARD（一种用于多源辐射状网络重构的算法）实例化了该框架。数值结果展示了该界的紧性，并量化了可行性与最优性之间的权衡。
英文摘要
Greedy algorithms efficiently approximate combinatorial optimization problems, but their guarantees weaken when feasibility couples combinatorial structure with global physical constraints. We study monotone nondecreasing supermodular minimization over the bases of a graphic greedoid under physics-induced constraints. We model physics-informed selection using a look-ahead oracle that identifies candidates extendable to a feasible basis, yielding the Conditioned Sequential Greedy Algorithm. We derive a closed-form approximation bound, which we call the price of feasibility, based on the variability of oracle-restricted candidate sets and a probabilistic correction for unobserved elements. As a case study, we show that FORWARD, an algorithm for multi-source radial network reconfiguration, instantiates this framework. Numerical results demonstrate the tightness of the bound and quantify the feasibility-optimality trade-off.
