Parameterized complexity of distance labeling and uniform channel assignment problems

Abstract 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 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 Fiala et al.: Parameterized complexity of coloring problems: Treewidth versus vertex cover. Finally, we show that the uniform variant of the Channel Assignment problem becomes NP -complete when generalized to graphs of bounded clique width.