Ganian, R and Ordyniak, S orcid.org/0000-0003-1935-651X (2019) The Power of Cut-Based Parameters for Computing Edge Disjoint Paths. In: Lecture Notes in Computer Science. WG 2019: Graph-Theoretic Concepts in Computer Science, 19-21 Jun 2019, Vall de Núria, Spain. Springer Verlag , pp. 190-204. ISBN 9783030307851
Abstract
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.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer Nature Switzerland AG 2019. This is an author produced version of a conference paper published in Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Edge disjoint path problem; Feedback edge set; Treecut width; Parameterized complexity |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Nov 2020 14:48 |
Last Modified: | 19 Dec 2020 02:50 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/978-3-030-30786-8_15 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:168077 |