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)


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.


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Burkard, R.E., Dlaska, K., Klinz, B.: The quickest flow problem. Mathematical Methods of Operations Research 37, 31–58 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Fleischer, L., Skutella, M.: Quickest flows over time. SIAM Journal on Computing 36, 1600–1630 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Fleischer, L.K., Tardos, É.: Efficient continuous-time dynamic network flow algorithms. Operations Research Letters 23, 71–80 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Ford, L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton (1962)zbMATHGoogle Scholar
  5. 5.
    Groß, Martin, Kappmeier, Jan-Philipp W., Schmidt, Daniel R., Schmidt, Melanie: Approximating Earliest Arrival Flows in Arbitrary Networks. In: Epstein, Leah, Ferragina, Paolo (eds.) ESA 2012. LNCS, vol. 7501, pp. 551–562. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  6. 6.
    Hausknecht, M., Au, T.-C., Stone, P., Fajardo, D., Waller. T.: Dynamic lane reversal in traffic management. In: 14th International IEEE Conference on Intelligent Transportation Systems (ITSC), pp. 1929–1934 (2011).Google Scholar
  7. 7.
    Hirsch, M.D., Papadimitriou, C.H., Vavasis, S.A.: Exponential lower bounds for finding brouwer fix points. Journal of Complexity 5, 379–416 (1989)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Hoppe, B., Tardos, É.: The quickest transshipment problem. Mathematics of Operations Research 25, 36–62 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Hoppe, B.E.: Efficient Dynamic Network Flow Algorithms. PhD thesis, Cornell University (1995).Google Scholar
  10. 10.
    Kim, S., Shekhar, S.: Contraflow network reconfiguration for evaluation planning: A summary of results. In: Proceedings of the 13th Annual ACM International Workshop on Geographic Information Systems, pp. 250–259 (2005).Google Scholar
  11. 11.
    Papadimitriou, C.H.: On the complexity of the parity argument and other inefficient proofs of existence. Journal of Computer and System Sciences 48, 498–532 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Rebennack, S., Arulselvan, A., Elefteriadou, L., Pardalos, P.M.: Complexity analysis for maximum flow problems with arc reversals. Journal of Combinatorial Optimization 19, 200–216 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Robbins, H.E.: A theorem on graphs, with an application to a problem of traffic control. The American Mathematical Monthly 46, 281–283 (1939)CrossRefGoogle Scholar
  14. 14.
    Skutella, M.: An introduction to network flows over time. In: Cook, W., Lovász, L., Vygen, J. (eds.) Research Trends in Combinatorial Optimization, pp. 451–482. Springer (2009).Google Scholar
  15. 15.
    Tjandra, S.A.: Dynamic network optimization with application to the evacuation problem. PhD thesis, Technical University of Kaiserslautern (2003).Google Scholar
  16. 16.
    Tuydes, H., Ziliaskopoulos, A.: Network re-design to optimize evacuation contraflow. In: Proceedings of the 83rd Annual Meeting of the Transportation Research Board, Washington, DC (2004).Google Scholar
  17. 17.
    Tuydes, H., Ziliaskopoulos, A.: Tabu-based heuristic approach for optimization of network evacuation contraflow. Transportation Research Record 1964, 157–168 (2006)CrossRefGoogle Scholar
  18. 18.
    Wolshon, B.: One-way-out: Contraflow freeway operation for hurricane evacuation. Natural Hazards Review 2, 105–112 (2001)CrossRefGoogle Scholar
  19. 19.
    Wolshon, B., Urbina, E., Levitan, M.: National review of hurricane evacuation plans and policies. LSU Hurricane Center, Louisiana State University, Baton Rouge, Louisiana, Technical report (2002)Google Scholar

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

Personalised recommendations