2026-08-10T18:26:10Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8255 2024-03-06T10:41:50Z ddc:004 open_access

On Structural Parameterizations of the Edge Disjoint Paths Problem Ganian, Robert Ordyniak, Sebastian Sridharan, Ramanujan edge disjoint path problem feedback vertex set treewidth fracture number parameterized complexity In this paper we revisit 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 focus lies on structural parameterizations for the problem that allow for efficient (polynomial-time or fpt) algorithms. As our first result, we answer an open question stated in Fleszar, Mnich, and Spoerhase (2016), by showing that the problem can be solved in polynomial time if the input graph has a feedback vertex set of size one. We also show that EDP parameterized by the treewidth and the maximum degree of the input graph is fixed-parameter tractable. Having developed two novel algorithms for EDP using structural restrictions on the input graph, we then turn our attention towards the augmented graph, i.e., the graph obtained from the input graph after adding one edge between every terminal pair. In constrast to the input graph, where EDP is known to remain NP-hard even for treewidth two, a result by Zhou et al. (2000) shows that EDP can be solved in non-uniform polynomial time if the augmented graph has constant treewidth; we note that the possible improvement of this result to an fpt-algorithm has remained open since then. We show that this is highly unlikely by establishing the W[1]-hardness of the problem parameterized by the treewidth (and even feedback vertex set) of the augmented graph. Finally, we develop an fpt-algorithm for EDP by exploiting a novel structural parameter of the augmented graph. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Robert Ganian and Sebastian Ordyniak and Ramanujan Sridharan 2017 Is Part Of LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2017.36 urn:nbn:de:0030-drops-82555 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.36 eng https://creativecommons.org/licenses/by/3.0/legalcode