The Power of Cut-Based Parameters for Computing Edge Disjoint
Paths

D 2019

The Power of Cut-Based Parameters for Computing Edge Disjoint Paths

GANIAN, Robert and Sebastian ORDYNIAK

Basic information

Original name

The Power of Cut-Based Parameters for Computing Edge Disjoint Paths

Authors

GANIAN, Robert (203 Czech Republic, guarantor, belonging to the institution) and Sebastian ORDYNIAK (276 Germany)

Edition

USA, WG 2019: Graph-Theoretic Concepts in Computer Science, p. 190-204, 15 pp. 2019

Publisher

Springer

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

References:

URL

Impact factor

Impact factor: 0.402 in 2005

RIV identification code

RIV/00216224:14330/19:00113728

Organization unit

Faculty of Informatics

ISBN

978-3-030-30785-1

ISSN

DOI

http://dx.doi.org/10.1007/978-3-030-30786-8_15

UT WoS

000557920500015

Keywords in English

Parameterized Complexity

Abstract

V originále

This paper revisits the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal pair in P. Our aim is to identify structural properties (parameters) of graphs which allow the efficient solution of EDP without restricting the placement of terminals in P in any way. In this setting, EDP is known to remain NP-hard even on extremely restricted graph classes, such as graphs with a vertex cover of size 3. We present three results which use edge-separator based parameters to chart new islands of tractability in the complexity landscape of EDP. Our first and main result utilizes the fairly recent structural parameter treecut width (a parameter with fundamental ties to graph immersions and graph cuts): we obtain a polynomial-time algorithm for EDP on every graph class of bounded treecut width. Our second result shows that EDP parameterized by treecut width is unlikely to be fixed-parameter tractable. Our final, third result is a polynomial kernel for EDP parameterized by the size of a minimum feedback edge set in the graph.

Citovat

GANIAN, Robert and Sebastian ORDYNIAK. The Power of Cut-Based Parameters for Computing Edge Disjoint Paths. Online. In Ignasi Sau and Dimitrios M. Thilikos. WG 2019: Graph-Theoretic Concepts in Computer Science. USA: Springer, 2019, p. 190-204. ISBN 978-3-030-30785-1. Available from: https://dx.doi.org/10.1007/978-3-030-30786-8_15.

@inproceedings{1648299,
   author = {Ganian, Robert and Ordyniak, Sebastian},
   address = {USA},
   booktitle = {WG 2019: Graph-Theoretic Concepts in Computer Science},
   doi = {http://dx.doi.org/10.1007/978-3-030-30786-8_15},
   editor = {Ignasi Sau and Dimitrios M. Thilikos},
   keywords = {Parameterized Complexity},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {USA},
   isbn = {978-3-030-30785-1},
   pages = {190-204},
   publisher = {Springer},
   title = {The Power of Cut-Based Parameters for Computing Edge Disjoint Paths},
   url = {https://link.springer.com/book/10.1007/978-3-030-30786-8#about},
   year = {2019}
}

TY  - JOUR
ID  - 1648299
AU  - Ganian, Robert - Ordyniak, Sebastian
PY  - 2019
TI  - The Power of Cut-Based Parameters for Computing Edge Disjoint Paths
PB  - Springer
CY  - USA
SN  - 9783030307851
KW  - Parameterized Complexity
UR  - https://link.springer.com/book/10.1007/978-3-030-30786-8#about
L2  - https://link.springer.com/book/10.1007/978-3-030-30786-8#about
N2  - This paper revisits the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal pair in P. Our aim is to identify structural properties (parameters) of graphs which allow the efficient solution of EDP without restricting the placement of terminals in P in any way. In this setting, EDP is known to remain NP-hard even on extremely restricted graph classes, such as graphs with a vertex cover of size 3. We present three results which use edge-separator based parameters to chart new islands of tractability in the complexity landscape of EDP. Our first and main result utilizes the fairly recent structural parameter treecut width (a parameter with fundamental ties to graph immersions and graph cuts): we obtain a polynomial-time algorithm for EDP on every graph class of bounded treecut width. Our second result shows that EDP parameterized by treecut width is unlikely to be fixed-parameter tractable. Our final, third result is a polynomial kernel for EDP parameterized by the size of a minimum feedback edge set in the graph.
ER  -

GANIAN, Robert and Sebastian ORDYNIAK. The Power of Cut-Based Parameters for Computing Edge Disjoint Paths. Online. In Ignasi Sau and Dimitrios M. Thilikos. \textit{WG 2019: Graph-Theoretic Concepts in Computer Science}. USA: Springer, 2019, p.~190-204. ISBN~978-3-030-30785-1. Available from: https://dx.doi.org/10.1007/978-3-030-30786-8\_{}15.

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