Graph orientations and flows over time

Ashwin Arulselvan, Martin Groß, Martin Skutella

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

2 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.
LanguageEnglish
Title of host publicationAlgorithms and Computation
Subtitle of host publication25th International Symposium, ISAAC 2014, Jeonju, Korea, December 15-17, 2014, Proceedings
EditorsHee-Kap Ahn, Chan-Su Shin
Place of PublicationCham
PublisherSpringer
Pages741-752
Number of pages12
ISBN (Print)9783319130743
DOIs
Publication statusPublished - 8 Nov 2014
Event25th International Symposium on Algorithms and Computation (ISAAC 2014) - Jeonju, Korea, Republic of
Duration: 15 Dec 201417 Dec 2014

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume8889

Conference

Conference25th International Symposium on Algorithms and Computation (ISAAC 2014)
CountryKorea, Republic of
CityJeonju
Period15/12/1417/12/14

Fingerprint

Flavors
Logistics

Keywords

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

Cite this

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 (pp. 741-752). (Lecture Notes in Computer Science; Vol. 8889). Cham: Springer. https://doi.org/10.1007/978-3-319-13075-0_58
Arulselvan, Ashwin ; Groß, Martin ; Skutella, Martin. / Graph orientations and flows over time. Algorithms and Computation: 25th International Symposium, ISAAC 2014, Jeonju, Korea, December 15-17, 2014, Proceedings. editor / Hee-Kap Ahn ; Chan-Su Shin. Cham : Springer, 2014. pp. 741-752 (Lecture Notes in Computer Science).
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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 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.",
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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 proceedingConference contribution book

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AU - Groß, Martin

AU - Skutella, Martin

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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.

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