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

(Extended Abstract)
  • Jiří Fiala
  • Tomáš Gavenčiak
  • Dušan Knop
  • Martin Koutecký
  • Jan Kratochvíl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)

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.

Notes

Acknowledgement

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

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Jiří Fiala
    • 1
  • Tomáš Gavenčiak
    • 1
  • Dušan Knop
    • 1
  • Martin Koutecký
    • 1
  • Jan Kratochvíl
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPragueCzech Republic

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