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- W2402083991 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 sf{FPT} algorithms previously parameterized by vertex cover, as is also demonstrated by our paper. We show that the {sc Uniform Channel Assignment} problem is fixed parameter tractable when parameterized by $nd$ and the largest weight and that every {sc $L(p_1, p_2,dots, p_k)$-labeling} problem is sf{FPT} when parameterized by $nd$, maximum $p_i$ and $k$. These results furthermore yield an sf{FPT} algorithms for {sc $L(p_1, p_2,dots, p_k)$-labeling} and {sc Channel Assignment} problems when parameterized by vertex cover size, answering an open question of Fiala et al.: {emph 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." @default.
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- W2402083991 date "2015-07-02" @default.
- W2402083991 modified "2023-09-27" @default.
- W2402083991 title "Distance constrained labeling on graphs with bounded neighborhood diversity." @default.
- W2402083991 hasPublicationYear "2015" @default.
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