Approximating the Network Design Problem for Potential-Based Flows

2026-04-29

AI Summary

This work addresses the design of potential flow networks—a class of optimization problems that are significantly harder than classical network flow due to their inherent nonlinearity. The paper presents the first effective approximation algorithm framework for this problem by introducing a refined reduction to well-studied combinatorial optimization problems such as constrained shortest paths, thereby enabling efficient solutions through existing algorithmic techniques. The study establishes matching complexity lower bounds that precisely delineate the approximability frontier of the problem and further demonstrates the NP-hardness and inapproximability of several key variants. Collectively, these results provide a comprehensive characterization of the computational complexity and algorithmic tractability of potential flow network design.

Abstract

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.

Problem

• network design
• potential-based flows
• nonlinearities
• energy transport networks
• combinatorial optimization

Innovation

• potential-based flows
• network design
• combinatorial optimization
• approximation algorithms
• computational complexity