Work

Planar Disjoint-Paths Completion

Year: 2015

Type: article

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 $f(k)\cdot n^{2}.$

Source: White Rose Research Online (University of Leeds, The University of Sheffield, University of York)

DOI: 10.48550/arxiv.1511.04952

Authors: Adler, Isolde, Kolliopoulos, Stavros G., Thilikos, Dimitrios M.

Institutions: Goethe University Frankfurt, National and Kapodistrian University of Athens, Centre National de la Recherche Scientifique, Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, European Social Fund

OpenAlex ID: W2951040374