The dominating set problem in geometric intersection graphs

M.T. de Berg, S. Kisfaludi-Bak, G. Woeginger

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Abstract

We study the parameterized complexity of dominating sets in geometric intersection graphs. In one dimension, we investigate intersection graphs induced by translates of a fixed pattern Q that consists of a finite number of intervals and a finite number of isolated points. We prove that Dominating Set on such intersection graphs is polynomially solvable whenever Q contains at least one interval, and whenever Q contains no intervals and for any two point pairs in Q the distance ratio is rational. The remaining case where Q contains no intervals but does contain an irrational distance ratio is shown to be NP-complete and contained in FPT (when parameterized by the solution size). In two and higher dimensions, we prove that Dominating Set is contained in W[1] for intersection graphs of semi-algebraic sets with constant description complexity. This generalizes known results from the literature. Finally, we establish W[1]-hardness for a large class of intersection graphs.
Original languageEnglish
Article number1709.05182
Number of pages19
JournalarXiv
Issue number1709.05182
Publication statusPublished - 2017

Keywords

  • Computational Geometry
  • Computational Complexity

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