Adler, I, Kolliopoulos, SG, Krause, PK et al. (3 more authors) (2017) Irrelevant vertices for the planar Disjoint Paths Problem. Journal of Combinatorial Theory, Series B, 122. pp. 815-843. ISSN 0095-8956
Abstract
The Disjoint Paths Problem asks, given a graph G and a set of pairs of terminals (s1,t1),…,(sk,tk)(s1,t1),…,(sk,tk), whether there is a collection of k pairwise vertex-disjoint paths linking sisi and titi, for i=1,…,ki=1,…,k. In their f(k)⋅n3f(k)⋅n3 algorithm for this problem, Robertson and Seymour introduced the irrelevant vertex technique according to which in every instance of treewidth greater than g(k)g(k) there is an “irrelevant” vertex whose removal creates an equivalent instance of the problem. This fact is based on the celebrated Unique Linkage Theorem , whose – very technical – proof gives a function g(k)g(k) that is responsible for an immense parameter dependence in the running time of the algorithm. In this paper we give a new and self-contained proof of this result that strongly exploits the combinatorial properties of planar graphs and achieves g(k)=O(k3/2⋅2k)g(k)=O(k3/2⋅2k). Our bound is radically better than the bounds known for general graphs.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2016, Elsevier. This is an author produced version of a paper published in Journal of Combinatorial Theory, Series B. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Graph Minors; Treewidth; Disjoint Paths Problem |
Dates: |
|
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: | 07 Nov 2016 15:58 |
Last Modified: | 02 Nov 2017 19:17 |
Published Version: | http://doi.org/10.1016/j.jctb.2016.10.001 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jctb.2016.10.001 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:107145 |