### Abstract

Language | English |
---|---|

Pages | 196-209 |

Number of pages | 14 |

Journal | Networks |

Volume | 66 |

Issue number | 3 |

Early online date | 6 Aug 2015 |

DOIs | |

Publication status | Published - 1 Oct 2015 |

Event | 25th International Symposium on Algorithms and Computation (ISAAC 2014) - Jeonju, Korea, Republic of Duration: 15 Dec 2014 → 17 Dec 2014 |

### Fingerprint

### Keywords

- dynamic flow
- flow over time
- graph orientation
- lane reversal

### Cite this

*Networks*,

*66*(3), 196-209. https://doi.org/10.1002/net.21623

}

*Networks*, vol. 66, no. 3, pp. 196-209. https://doi.org/10.1002/net.21623

**Graph orientation and flows over time.** / Arulselvan, Ashwin; Groß, Martin; Skutella, Martin.

Research output: Contribution to journal › Article

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

VL - 66

SP - 196

EP - 209

JO - Networks

T2 - Networks

JF - Networks

SN - 0028-3045

IS - 3

ER -