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arXiv · 1511.04952

Planar Disjoint-Paths Completion

Isolde Adler·Stavros G. Kolliopoulos·Dimitrios M. Thilikos
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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 $G,$ $k$ 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 $f(k)\cdot n^{2}.$

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Isolde Adler, Stavros G. Kolliopoulos, Dimitrios M. Thilikos. 2015-11-17. Planar Disjoint-Paths Completion. https://arxiv.org/abs/1511.04952

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