Fixed Parameter Complexity of Distance Constrained Labeling and Uniform Channel Assignment Problems

(Extended Abstract)
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)


We study computational complexity of the class of distance-constrained 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 \(L(p_1, p_2,\dots , p_k){\text {-}}{\textsc {labeling}}\) problem is FPT when parameterized by the neighborhood diversity, the maximum \(p_i\) 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.


Channel Assignment Problem Bounded Clique Width fixed-parameter Tractable Variable Neighborhood Bounded Vertex Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank Andrzej Proskurowski, Tomáš Masařík and anonymous referees for valuable comments.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Applied MathematicsCharles UniversityPragueCzech Republic

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