Graph orientations and flows over time

Ashwin Arulselvan; Martin Groß; Martin Skutella

doi:10.1007/978-3-319-13075-0_58

Graph orientations and flows over time

Ashwin Arulselvan, Martin Groß, Martin Skutella

Management Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

3 Citations (Scopus)

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 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 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.

Original language	English
Title of host publication	Algorithms and Computation
Subtitle of host publication	25th International Symposium, ISAAC 2014, Jeonju, Korea, December 15-17, 2014, Proceedings
Editors	Hee-Kap Ahn, Chan-Su Shin
Place of Publication	Cham
Publisher	Springer
Pages	741-752
Number of pages	12
ISBN (Print)	9783319130743
DOIs	https://doi.org/10.1007/978-3-319-13075-0_58
Publication status	Published - 8 Nov 2014
Event	25th International Symposium on Algorithms and Computation (ISAAC 2014) - Jeonju, Korea, Republic of Duration: 15 Dec 2014 → 17 Dec 2014

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	8889

Conference

Conference	25th International Symposium on Algorithms and Computation (ISAAC 2014)
Country/Territory	Korea, Republic of
City	Jeonju
Period	15/12/14 → 17/12/14

Keywords

artificial intelligence
computers
graph orientations
multi-commodity
network flows
non-approximability
reversal problems
routing problems
single source
time horizons
flow graphs

Access to Document

10.1007/978-3-319-13075-0_58

Cite this

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title = "Graph orientations and flows over time",

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 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 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.",

keywords = "artificial intelligence, computers, graph orientations, multi-commodity, network flows, non-approximability, reversal problems, routing problems, single source, time horizons, flow graphs",

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Arulselvan, A, Groß, M & Skutella, M 2014, Graph orientations and flows over time. in H-K Ahn & C-S Shin (eds), Algorithms and Computation: 25th International Symposium, ISAAC 2014, Jeonju, Korea, December 15-17, 2014, Proceedings. Lecture Notes in Computer Science, vol. 8889, Springer, Cham, pp. 741-752, 25th International Symposium on Algorithms and Computation (ISAAC 2014), Jeonju, Korea, Republic of, 15/12/14. https://doi.org/10.1007/978-3-319-13075-0_58

Graph orientations and flows over time. / Arulselvan, Ashwin; Groß, Martin; Skutella, Martin.
Algorithms and Computation: 25th International Symposium, ISAAC 2014, Jeonju, Korea, December 15-17, 2014, Proceedings. ed. / Hee-Kap Ahn; Chan-Su Shin. Cham: Springer, 2014. p. 741-752 (Lecture Notes in Computer Science; Vol. 8889).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - Graph orientations and flows over time

AU - Arulselvan, Ashwin

AU - Groß, Martin

AU - Skutella, Martin

PY - 2014/11/8

Y1 - 2014/11/8

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 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 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.

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 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 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.

KW - artificial intelligence

KW - computers

KW - graph orientations

KW - multi-commodity

KW - network flows

KW - non-approximability

KW - reversal problems

KW - routing problems

KW - single source

KW - time horizons

KW - flow graphs

UR - http://dx.doi.org/10.1007/978-3-319-13075-0

UR - http://tcs.postech.ac.kr/isaac2014/index

U2 - 10.1007/978-3-319-13075-0_58

DO - 10.1007/978-3-319-13075-0_58

M3 - Conference contribution book

SN - 9783319130743

T3 - Lecture Notes in Computer Science

SP - 741

EP - 752

BT - Algorithms and Computation

A2 - Ahn, Hee-Kap

A2 - Shin, Chan-Su

PB - Springer

CY - Cham

T2 - 25th International Symposium on Algorithms and Computation (ISAAC 2014)

Y2 - 15 December 2014 through 17 December 2014

ER -

Graph orientations and flows over time

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Keywords

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Graph orientation and flows over time

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