Variants of Plane Diameter Completion - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier
Communication Dans Un Congrès Année : 2015

Variants of Plane Diameter Completion

Résumé

The {\sc Plane Diameter Completion} problem asks, given a plane graph $G$ and a positive integer $d$, if it is a spanning subgraph of a plane graph $H$ that has diameter at most $d$. We examine two variants of this problem where the input comes with another parameter $k$. In the first variant, called BPDC, $k$ upper bounds the total number of edges to be added and in the second, called BFPDC, $k$ upper bounds the number of additional edges per face. We prove that both problems are {\sf NP}-complete, the first even for 3-connected graphs of face-degree at most 4 and the second even when $k=1$ on 3-connected graphs of face-degree at most 5. In this paper we give parameterized algorithms for both problems that run in $O(n^{3})+2^{2^{O((kd)^2\log d)}}\cdot n$ steps.
Fichier principal
Vignette du fichier
6.pdf (639.2 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

lirmm-01225566 , version 1 (16-03-2018)

Licence

Identifiants

Citer

Clément Requilé, Dimitrios M. Thilikos, Petr A. Golovach. Variants of Plane Diameter Completion. IPEC 2015 - 10th International Symposium on Parameterized and Exact Computation, Sep 2015, Patras, Greece. pp.30-42, ⟨10.4230/LIPIcs.IPEC.2015.30⟩. ⟨lirmm-01225566⟩
284 Consultations
113 Téléchargements

Altmetric

Partager

More