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

Beitrag in einer Fachzeitschrift

Details zur Publikation

Autorinnen und Autoren: Groß M, Pfetsch ME, Schewe L, Schmidt M, Skutella M
Zeitschrift: Networks
Jahr der Veröffentlichung: 2018
ISSN: 0028-3045
eISSN: 1097-0037
Sprache: Englisch


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-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Schewe, Lars PD Dr.
Lehrstuhl für Angewandte Mathematik (Gemischt-ganzzahlige lineare und nichtlineare Optimierung)
Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen

Einrichtungen weiterer Autorinnen und Autoren

Technische Universität Berlin
Technische Universität Darmstadt


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).


Zuletzt aktualisiert 2019-03-01 um 09:10