We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow problems, the nonlinearities inherent in potential-based networks introduce significant new challenges. We address these challenges through intricate reductions to classical combinatorial optimization problems, such as (constrained) shortest path problems, enabling the application of well-established algorithmic techniques to compute exact and approximate solutions efficiently. Finally, we complement these algorithmic results with matching complexity results concerning the hardness and non-approximability of the considered problem variants.

翻译：我们针对势基流模型中一类基础性网络设计问题开发了高效算法，该模型是众多能源传输网络（如氢能网络和电力网络）的核心要素。与经典网络流问题不同，势基网络固有的非线性特性带来了重大新挑战。我们通过巧妙地将问题归约为经典组合优化问题（如（带约束的）最短路径问题）来应对这些挑战，从而能够运用成熟的算法技术高效计算精确解与近似解。最后，我们通过匹配的复杂度结果（涉及所考虑问题变体的难解性与不可近似性）对上述算法成果进行了补充。