an:06937761
Zbl 1395.05143
Fiala, Ji????; Gaven??iak, Tom????; Knop, Du??an; Kouteck??, Martin; Kratochv??l, Jan
Parameterized complexity of distance labeling and uniform channel assignment problems
EN
Discrete Appl. Math. 248, 46-55 (2018).
00414462
2018
j
05C78 05C82 05C12 90B80
distance labeling; channel assignment; bounded cliquewidth; bounded vertex cover; fixed parameter tractability
Summary: We rephrase the distance labeling problem as a specific uniform variant of the channel assignment problem and show that the latter one is fixed parameter tractable when parameterized by the neighborhood diversity together with the largest weight. Consequently, the distance labeling problem is \(\mathsf{FPT}\) when parameterized by the neighborhood diversity, the maximum \(p_i\) and \(k\). This is indeed a more general answer to an open question of \textit{J. Fiala} et al. [Lect. Notes Comput. Sci. 5532, 221--230 (2009; Zbl 1241.68071)].
Finally, we show that the uniform variant of the channel assignment problem becomes \(\mathsf{NP}\)-complete when generalized to graphs of bounded clique width.
Zbl 1241.68071