Adler, I, Kolliopoulos, SG and Thilikos, DM (2016) Planar Disjoint-Paths Completion. Algorithmica, 76 (2). pp. 401-425. ISSN 0178-4617
Abstract
We introduce Planar Disjoint Paths Completion, a completion counterpart of the Disjoint Paths problem, and study its parameterized complexity. The problem can be stated as follows: given a, not necessarily connected, plane graph G, k pairs of terminals, and a face F of G, find a minimum-size set of edges, if one exists, to be added inside F so that the embedding remains planar and the pairs become connected by k disjoint paths in the augmented network. Our results are twofold: first, we give an upper bound on the number of necessary additional edges when a solution exists. This bound is a function of k, independent of the size of G. Second, we show that the problem is fixed-parameter tractable, in particular, it can be solved in time f(k) · n2.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015, Springer Science+Business Media New York. This is an author produced version of a paper published in Algorithmica. The final publication is available at Springer via http://dx.doi.org/10.1007/s00453-015-0046-2. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Completion problems, Disjoint paths, Planar graphs |
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) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 Sep 2016 14:10 |
Last Modified: | 16 Jan 2018 08:02 |
Published Version: | http://dx.doi.org/10.1007/s00453-015-0046-2 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00453-015-0046-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:104729 |