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On the Robustness of Potential-Based Flow Networks

Submission Status:under review
  • Potential-based flows provide a simple yet realistic mathematical model of transport in many real-world infrastructure networks such as, e.g., electricity, gas, or water networks, where the flow along each edge is controlled via the (difference of) potentials at its end nodes. A potential-based flow network is robust if the maximal difference of node potentials needed to satisfy a set of demands cannot increase if demands are decreased. This notion of robustness is motivated by infrastructure networks where users first make reservations for certain demands that may be larger than the actual amounts sent later on. Here node potentials correspond to physical quantities such as the pressures or the voltages and must be guaranteed to lie within a fixed range, even if the actual amounts are smaller than the previously reserved demands. Our main results are a precise characterization of such robust networks for the case of point-to-point demands via forbidden node-labeled graph minors, as well as an efficient algorithm for testing robustness.

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Metadaten
Author:Max Klimm, Marc Pfetsch, Rico Raber, Martin Skutella
Document Type:Preprint
Language:English
Date of Publication (online):2020/02/24
Release Date:2020/02/24
Institutes:Technische Universität Darmstadt
Humboldt-Universität zu Berlin
Technische Universität Berlin
Subprojects:A07
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International