On the robustness of potential-based flow networks

Potential-based flows provide a simple yet realistic mathematical model of transport in many real-world infrastructure networks such as, e.g., gas or water networks, where the flow along each edge depends on the difference of the potentials at its end nodes. We call a network topology robust if the...

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Veröffentlicht in:Mathematical programming Jg. 197; H. 1; S. 337 - 374
Hauptverfasser: Klimm, Max, Pfetsch, Marc E., Raber, Rico, Skutella, Martin
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2023
Schlagworte:
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Theoretical
05C21
90B10
90C35
05C83
Node-labeled graph minors
Potential-based network flows
Robustness
ISSN:0025-5610, 1436-4646
Online-Zugang:Volltext
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Zusammenfassung:Potential-based flows provide a simple yet realistic mathematical model of transport in many real-world infrastructure networks such as, e.g., gas or water networks, where the flow along each edge depends on the difference of the potentials at its end nodes. We call a network topology robust if the maximal node potential needed to satisfy a set of demands never increases when 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 flows sent later on. In these networks, node potentials correspond to physical quantities such as pressures or hydraulic heads 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 robust network topologies for the case of point-to-point demands via forbidden node-labeled graph minors, as well as an efficient algorithm for testing robustness.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-021-01760-w