Vertex Disjoint Paths for Dispatching in Railways

Holger Flier; Matúš Mihalák; Anita Schöbel; Peter Widmayer; Anna Zych

doi:10.4230/OASIcs.ATMOS.2010.61

Vertex Disjoint Paths for Dispatching in Railways

Holger Flier, Matúš Mihalák, Anita Schöbel, Peter Widmayer, Anna Zych

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization, and routing-in-rounds problem. Although all considered variants are NP-hard in planar graphs, restrictions on the location of the terminals, motivated by railway applications, lead to polynomially solvable cases for the decision and maximization versions of the problem, and to a $p$-approximation algorithm for the routing-in-rounds problem, where $p$ is the maximum number of alternative paths for a terminal pair.

Original language	English
Title of host publication	Proceedings of the 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS)
Pages	61-73
Number of pages	13
DOIs	https://doi.org/10.4230/OASIcs.ATMOS.2010.61
Publication status	Published - 2010
Externally published	Yes

Access to Document

10.4230/OASIcs.ATMOS.2010.61

Cite this

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title = "Vertex Disjoint Paths for Dispatching in Railways",

abstract = "We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization, and routing-in-rounds problem. Although all considered variants are NP-hard in planar graphs, restrictions on the location of the terminals, motivated by railway applications, lead to polynomially solvable cases for the decision and maximization versions of the problem, and to a $p$-approximation algorithm for the routing-in-rounds problem, where $p$ is the maximum number of alternative paths for a terminal pair.",

author = "Holger Flier and Mat{\'u}{\v s} Mihal{\'a}k and Anita Sch{\"o}bel and Peter Widmayer and Anna Zych",

year = "2010",

doi = "10.4230/OASIcs.ATMOS.2010.61",

language = "English",

isbn = "978-3-939897-20-0",

pages = "61--73",

booktitle = "Proceedings of the 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS)",

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Vertex Disjoint Paths for Dispatching in Railways. / Flier, Holger; Mihalák, Matúš; Schöbel, Anita et al.
Proceedings of the 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS). 2010. p. 61-73.

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

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T1 - Vertex Disjoint Paths for Dispatching in Railways

AU - Flier, Holger

AU - Mihalák, Matúš

AU - Schöbel, Anita

AU - Widmayer, Peter

AU - Zych, Anna

PY - 2010

Y1 - 2010

N2 - We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization, and routing-in-rounds problem. Although all considered variants are NP-hard in planar graphs, restrictions on the location of the terminals, motivated by railway applications, lead to polynomially solvable cases for the decision and maximization versions of the problem, and to a $p$-approximation algorithm for the routing-in-rounds problem, where $p$ is the maximum number of alternative paths for a terminal pair.

AB - We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization, and routing-in-rounds problem. Although all considered variants are NP-hard in planar graphs, restrictions on the location of the terminals, motivated by railway applications, lead to polynomially solvable cases for the decision and maximization versions of the problem, and to a $p$-approximation algorithm for the routing-in-rounds problem, where $p$ is the maximum number of alternative paths for a terminal pair.

U2 - 10.4230/OASIcs.ATMOS.2010.61

DO - 10.4230/OASIcs.ATMOS.2010.61

M3 - Conference article in proceeding

SN - 978-3-939897-20-0

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EP - 73

BT - Proceedings of the 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS)

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