Abstract
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.
Paper supported by project Kontakt LH12095 and by GAUK project 1784214.
Second, third and fourth authors are supported by the project SVV-2016-260332. First, third and fifth authors are supported by project CE-ITI P202/12/G061 of GAČR.
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We thank Andrzej Proskurowski, Tomáš Masařík and anonymous referees for valuable comments.
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Fiala, J., Gavenčiak, T., Knop, D., Koutecký, M., Kratochvíl, J. (2016). Fixed Parameter Complexity of Distance Constrained Labeling and Uniform Channel Assignment Problems. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_6
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DOI: https://doi.org/10.1007/978-3-319-42634-1_6
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