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 pairs of terminals, and a face of find a minimum-size set of edges, if one exists, to be added inside so that the embedding remains planar and the pairs become connected by 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 , independent of the size of Second, we show that the problem is fixed-parameter tractable, in particular, it can be solved in time
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}
}