Fixed parameter complexity of distance constrained labeling and uniform channel assignment problems

Abstract

We study computational complexity of the class of distanceconstrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance constrained graph labeling problem as a specific uniform variant of the Channel Assignment problem and show that this problem is fixed parameter tractable when parameterized by the neighborhood diversity together with the largest weight. Consequently, every L(p1, p2,…, pk)-labeling problem is FPT when parameterized by the neighborhood diversity, the maximum pi and k. Finally, we show that the uniform variant of the Channel Assignment problem becomes NP-complete when generalized to graphs of bounded clique width.