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.
Supported by the DFG Priority Program Algorithms for Big Data (SPP 1736) and by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin. See also http://arxiv.org/abs/1409.3081 for a version of this paper with all proofs.
Ashwin Arulselvan: The work was performed while the author was working at TU Berlin.
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Arulselvan, A., Groß, M., Skutella, M. (2014). Graph Orientation and Flows over Time. In: Ahn, HK., Shin, CS. (eds) Algorithms and Computation. ISAAC 2014. Lecture Notes in Computer Science(), vol 8889. Springer, Cham. https://doi.org/10.1007/978-3-319-13075-0_58
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DOI: https://doi.org/10.1007/978-3-319-13075-0_58
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