Algorithmic results for potential-based flows: Easy and hard cases

Martin Gross, Marc E. Pfetsch, Lars Schewe, Martin Schmidt*, Martin Skutella

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.

Original languageEnglish
Pages (from-to)306-324
Number of pages19
Issue number3
Publication statusPublished - 24 Dec 2018

Keywords / Materials (for Non-textual outputs)

  • maximum flow problem
  • network reduction
  • NP-hardness
  • potential networks
  • potential-based flows
  • series-parallel graphs


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