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Martin Groß (mgrobuwaterloo.ca) Abstract: Potentialbased 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 NPhard. Nevertheless, for particular seriesparallel networks, one can use algorithms for the subset sum problem. Moreover, applying network presolving based on generalized seriesparallel structures allows to significantly reduce the size of realistic energy networks. Keywords: Potential networks, Potentialbased flows, Maximum flow problem, Seriesparallel graphs, Network reduction, NPhardness Category 1: Network Optimization Category 2: Integer Programming Category 3: Applications  Science and Engineering Citation: Download: [PDF] Entry Submitted: 08/04/2017 Modify/Update this entry  
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