English

Planar Disjoint-Paths Completion

Data Structures and Algorithms 2015-11-18 v2 Combinatorics

Abstract

introduce {\sc 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,G, kk pairs of terminals, and a face FF of G,G, find a minimum-size set of edges, if one exists, to be added inside FF so that the embedding remains planar and the pairs become connected by kk 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 kk, independent of the size of G.G. Second, we show that the problem is fixed-parameter tractable, in particular, it can be solved in time f(k)n2.f(k)\cdot n^{2}.

Keywords

Cite

@article{arxiv.1511.04952,
  title  = {Planar Disjoint-Paths Completion},
  author = {Isolde Adler and Stavros G. Kolliopoulos and Dimitrios M. Thilikos},
  journal= {arXiv preprint arXiv:1511.04952},
  year   = {2015}
}
R2 v1 2026-06-22T11:46:14.042Z