Approximating the Network Design Problem for Potential-Based Flows

TL;DR

This paper introduces efficient algorithms for a key network design problem in potential-based flow models, addressing nonlinear challenges and establishing complexity bounds.

Contribution

It presents novel reductions to classical optimization problems and provides both algorithmic solutions and complexity results for potential-based network design.

Findings

Algorithms for exact and approximate solutions developed.

Reductions to shortest path problems enable efficient computation.

Complexity results show hardness and non-approximability of variants.

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.