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Graph orientation and flows over time
Author(s) -
Arulselvan Ashwin,
Groß Martin,
Skutella Martin
Publication year - 2015
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.21623
Subject(s) - flow network , orientation (vector space) , computer science , time horizon , flow (mathematics) , routing (electronic design automation) , upper and lower bounds , graph , undirected graph , multi commodity flow problem , mathematical optimization , mathematics , theoretical computer science , geometry , computer network , mathematical analysis
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. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 66(3), 196–209 2015