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Graph Orientation and Flows over Time

  • Ashwin Arulselvan
  • Martin Groß
  • Martin Skutella
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8889)

Abstract

Flows over time are used to model many real-world logistic and routing problems. The networks underlying such problems – streets, tracks, etc. – are inherently undirected and directions are only imposed on them to reduce the danger of colliding vehicles and similar problems. Thus the question arises, what influence the orientation of the network has on the network flow over time problem that is being solved on the oriented network. In the literature, this is also referred to as the contraflow or lane reversal problem.

We introduce and analyze the price of orientation: How much flow is lost in any orientation of the network if the time horizon remains fixed? We prove that there is always an orientation where we can still send \(\frac{1}{3}\) of the flow and this bound is tight. For the special case of networks with a single source or sink, this fraction is \(\frac{1}{2}\) which is again tight. We present more results of similar flavor and also show non-approximability results for finding the best orientation for single and multicommodity maximum flows over time.

Keywords

Time Horizon Time Problem Directed Network Full Version Undirected Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ashwin Arulselvan
    • 1
  • Martin Groß
    • 2
  • Martin Skutella
    • 2
  1. 1.Department of Management ScienceUniversity of StrathclydeGlasgowUK
  2. 2.Institut für MathematikTU BerlinBerlinGermany

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