Fixed Parameter Complexity of Distance Constrained Labeling and Uniform Channel Assignment Problems - (Extended Abstract)

We study the complexity of a group of distance-constrained graph labeling problems when parameterized by the neighborhood diversity (nd), which is a natural graph parameter between vertex cover and clique width. Neighborhood diversity has been used to generalize and speed up FPT algorithms previously parameterized by vertex cover, as is also demonstrated by our paper. We show that the Uniform Channel Assignment problem is fixed parameter tractable when parameterized by nd and the largest weight and that every L(p1, p2, . . . , pk)-labeling problem is FPT when parameterized by nd, maximum pi and k. These results furthermore yield an FPT algorithms for L(p1, p2, . . . , pk)-labeling and Channel Assignment problems when parameterized by vertex cover size, answering an open question of Fiala et al.: Parameterized complexity of coloring problems: Treewidth versus vertex cover, generalizing their results beyond L(2, 1)-labeling, and tightening the complexity gap to clique width, where the problems are already hard for constant clique width. 1998 ACM Subject Classification G.2.2 Graph Theory