TY - JOUR A1 - Labbé, Martine A1 - Plein, Fränk A1 - Schmidt, Martin A1 - Thürauf, Johannes T1 - Deciding Feasibility of a Booking in the European Gas Market on a Cycle is in P for the Case of Passive Networks JF - Networks N2 - 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. KW - Gas networks KW - European entry-exit market KW - Bookings KW - Potential-based flows KW - Computational complexity Y1 - 2019 U6 - https://doi.org/10.1007/s00186-021-00752-y VL - 78 IS - 2 SP - 128 EP - 152 ER -