Graph orientation and flows over time

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Arulselvan, Ashwin and Groß, Martin and Skutella, Martin (2015) Graph orientation and flows over time. Networks, 66 (3). pp. 196-209. ISSN 1097-0037 (https://doi.org/10.1002/net.21623)

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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 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.

ORCID iDs

Arulselvan, Ashwin ORCID logoORCID: https://orcid.org/0000-0001-9772-5523, Groß, Martin and Skutella, Martin;
  • Item type:Article
    ID code:55782
    Dates:
    Date
    Event
    1 October 2015
    Published
    6 August 2015
    Published Online
    1 June 2015
    Accepted
    Notes:This is the peer reviewed version of the following article: Arulselvan, A., Groß, M. and Skutella, M. (2015), Graph orientation and flows over time. Networks, 66: 196–209, which has been published in final form at http://dx.doi.org/doi: 10.1002/net.21623. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. "An extended abstract has appeared in proceedings of the 25th International Symposium on Algorithms and Computation (ISAAC '14)."
    Subjects:Science > Mathematics > Electronic computers. Computer science
    Department:Strathclyde Business School > Management Science
    Depositing user: Pure Administrator
    Date deposited:07 Mar 2016 15:00
    Last modified:12 Dec 2024 03:33
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/55782
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