The Maximum Flow Problem for Oriented Flows

Authors Stanley Schade, Martin Strehler

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Stanley Schade
Martin Strehler

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Stanley Schade and Martin Strehler. The Maximum Flow Problem for Oriented Flows. In 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016). Open Access Series in Informatics (OASIcs), Volume 54, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


In several applications of network flows, additional constraints have to be considered. In this paper, we study flows, where the flow particles have an orientation. For example, cargo containers with doors only on one side and train coaches with 1st and 2nd class compartments have such an orientation. If the end position has a mandatory orientation, not every path from source to sink is feasible for routing or additional transposition maneuvers have to be made. As a result, a source-sink path may visit a certain vertex several times. We describe structural properties of optimal solutions, determine the computational complexity, and present an approach for approximating such flows.
  • network flow with orientation
  • graph expansion
  • approximation
  • container logistics
  • train routing


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