286 2019 2021 eng 128 152 25 2 78 article 1 2019-11-12 2019-11-12 -- We show that the feasibility of a booking in the European entry-exit gas market can be decided in polynomial time on single-cycle networks that are passive, i.e., do not contain controllable elements. The feasibility of a booking can be characterized by solving polynomially many nonlinear potential-based flow models for computing so-called potential-difference maximizing load flow scenarios. We thus analyze the structure of these models and exploit both the cyclic graph structure as well as specific properties of potential-based flows. This enables us to solve the decision variant of the nonlinear potential-difference maximization by reducing it to a system of polynomials of constant dimension that is independent of the cycle's size. This system of fixed dimension can be handled with tools from real algebraic geometry to derive a polynomial-time algorithm. The characterization in terms of potential-difference maximizing load flow scenarios then leads to a polynomial-time algorithm for deciding the feasibility of a booking. Our theoretical results extend the existing knowledge about the complexity of deciding the feasibility of bookings from trees to single-cycle networks. Networks 10.1007/s00186-021-00752-y Published 2 Creative Commons - CC BY - Namensnennung 4.0 International Martine Labbé Fränk Plein Martin Schmidt Johannes Thürauf eng uncontrolled Gas networks eng uncontrolled European entry-exit market eng uncontrolled Bookings eng uncontrolled Potential-based flows eng uncontrolled Computational complexity Friedrich-Alexander-Universität Erlangen-Nürnberg A05 B07 Z01 B08 Universität Trier Université libre de Bruxelles https://opus4.kobv.de/opus4-trr154/files/286/preprint-version-2020-11-20.pdf