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On structural parameterizations of the edge disjoint paths problem
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Ganian, Robert, Ordyniak, Sebastian and Ramanujan, Maadapuzhi Sridharan (2021) On structural parameterizations of the edge disjoint paths problem. Algorithmica, 83 (6). pp. 1605-1637. doi:10.1007/s00453-020-00795-3 ISSN 1432-0541.
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Official URL: https://doi.org/10.1007/s00453-020-00795-3
Abstract
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 et al. (Proceedings of the ESA, 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. (Algorithmica 26(1):3--30, 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.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software T Technology > T Technology (General) |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||||||||
| SWORD Depositor: | Library Publications Router | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Graph theory -- Data processing , Computer algorithms, Combinatorial analysis, Computer graphics, Graph algorithms | ||||||||||||
| Journal or Publication Title: | Algorithmica | ||||||||||||
| Publisher: | Springer Nature | ||||||||||||
| ISSN: | 1432-0541 | ||||||||||||
| Official Date: | June 2021 | ||||||||||||
| Dates: |
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| Volume: | 83 | ||||||||||||
| Number: | 6 | ||||||||||||
| Page Range: | pp. 1605-1637 | ||||||||||||
| DOI: | 10.1007/s00453-020-00795-3 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
| Date of first compliant deposit: | 17 February 2022 | ||||||||||||
| Date of first compliant Open Access: | 21 February 2022 | ||||||||||||
| RIOXX Funder/Project Grant: |
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| Is Part Of: | 1 |
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