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

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autor(en): Groß M, Pfetsch ME, Schewe L, Schmidt M, Skutella M
Zeitschrift: Networks
Jahr der Veröffentlichung: 2018
ISSN: 0028-3045
eISSN: 1097-0037
Sprache: Englisch


Abstract


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-Autoren / FAU-Herausgeber

Schewe, Lars PD Dr.
Lehrstuhl für Wirtschaftsmathematik
Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen


Autor(en) der externen Einrichtung(en)
Technische Universität Berlin
Technische Universität Darmstadt


Zitierweisen

APA:
Groß, M., Pfetsch, M.E., Schewe, L., Schmidt, M., & Skutella, M. (2018). Algorithmic Results for Potential-Based Flows: Easy and Hard Cases. Networks. https://dx.doi.org/10.1002/net.21865

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

BibTeX: 

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