TY - JOUR
T1 - Graph orientation and flows over time
AU - Arulselvan, Ashwin
AU - Groß, Martin
AU - Skutella, Martin
N1 - 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)."
PY - 2015/10/1
Y1 - 2015/10/1
N2 - 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.
AB - 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.
KW - dynamic flow
KW - flow over time
KW - graph orientation
KW - lane reversal
UR - http://www.scopus.com/inward/record.url?scp=84941174057&partnerID=8YFLogxK
UR - http://tcs.postech.ac.kr/isaac2014/index
U2 - 10.1002/net.21623
DO - 10.1002/net.21623
M3 - Article
AN - SCOPUS:84941174057
SN - 0028-3045
VL - 66
SP - 196
EP - 209
JO - Networks
JF - Networks
IS - 3
T2 - 25th International Symposium on Algorithms and Computation (ISAAC 2014)
Y2 - 15 December 2014 through 17 December 2014
ER -