Journal
NETWORKS
Volume 73, Issue 3, Pages 306-324Publisher
WILEY
DOI: 10.1002/net.21865
Keywords
maximum flow problem; network reduction; NP-hardness; potential-based flows; potential networks; series-parallel graphs
Funding
- Bayerisches Staatsministerium fur Wirtschaft und Medien, Energie und Technologie
- Deutsche Forschungsgemeinschaft [TRR 154]
- Einstein Stiftung Berlin
- Bavarian State Government
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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.
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