Algorithmic Results for Potential-Based Flows: Easy and Hard Cases

Journal article

Publication Details

Author(s): Groß M, Pfetsch ME, Schewe L, Schmidt M, Skutella M
Journal: Networks
Publication year: 2018
ISSN: 0028-3045
eISSN: 1097-0037
Language: English


Potential-based flows are an extension of classical network flows in which the flow on an arc is determined by the difference of the potentials of its incident nodes. Such flows are unique and arise, for example, in energy networks. Two important algorithmic problems are to determine whether there exists a feasible flow and to maximize the flow between two designated nodes. We show that these problems can be solved for the single source and sink case by reducing the network to a single arc. However, if we additionally consider switches that allow to force the flow to 0 and decouple the potentials, these problems are NP-hard. Nevertheless, for particular series-parallel networks, one can use algorithms for the subset sum problem. Moreover, applying network presolving based on generalized series-parallel structures allows to significantly reduce the size of realistic energy networks.

FAU Authors / FAU Editors

Schewe, Lars PD Dr.
Economics - Discrete Optimization - Mathematics (EDOM)
Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen

External institutions with authors

Technische Universität Berlin
Technische Universität Darmstadt

How to cite

Groß, M., Pfetsch, M.E., Schewe, L., Schmidt, M., & Skutella, M. (2018). Algorithmic Results for Potential-Based Flows: Easy and Hard Cases. Networks.

Groß, Martin, et al. "Algorithmic Results for Potential-Based Flows: Easy and Hard Cases." Networks (2018).


Last updated on 2019-03-01 at 09:10