Graph orientation and flows over time

Ashwin Arulselvan, Martin Groß, Martin Skutella

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
118 Downloads (Pure)


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 one-third of the flow and this bound is tight. For the special case of networks with a single source or sink, this fraction is half, which is again tight. We present more results of similar flavor and also show nonapproximability results for finding the best orientation for single and multicommodity maximum flows over time.
Original languageEnglish
Pages (from-to)196-209
Number of pages14
Issue number3
Early online date6 Aug 2015
Publication statusPublished - 1 Oct 2015
Event25th International Symposium on Algorithms and Computation (ISAAC 2014) - Jeonju, Korea, Republic of
Duration: 15 Dec 201417 Dec 2014


  • dynamic flow
  • flow over time
  • graph orientation
  • lane reversal


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  • Graph orientations and flows over time

    Arulselvan, A., Groß, M. & Skutella, M., 8 Nov 2014, Algorithms and Computation: 25th International Symposium, ISAAC 2014, Jeonju, Korea, December 15-17, 2014, Proceedings. Ahn, H-K. & Shin, C-S. (eds.). Cham: Springer, p. 741-752 12 p. (Lecture Notes in Computer Science; vol. 8889).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution book

    3 Citations (Scopus)

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