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Kick the Cliques

Authors Gaétan Berthe , Marin Bougeret , Daniel Gonçalves , Jean-Florent Raymond

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LIPIcs.IPEC.2024.13.pdf
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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Computational geometry
Keywords
  • Subexponential FPT algorithms
  • implicit hitting set problems
  • geometric intersection graphs

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Abstract

In the K_r-Hitting problem, given a graph G and an integer k one has to decide if there exists a set of at most k vertices whose removal destroys all r-cliques of G.
In this paper we give an algorithm for K_r-Hitting that runs in subexponential FPT time on graph classes satisfying two simple conditions related to cliques and treewidth. As an application we show that our algorithm solves K_r-Hitting in time  
- 2^{O_r(k^{(r+1)/(r+2)}log k)} ⋅ n^{O_r(1)} in pseudo-disk graphs and map-graphs; 
- 2^{O_{t,r}(k^{2/3}log k)} ⋅ n^{O_r(1)} in K_{t,t}-subgraph-free string graphs; and 
- 2^{O_{H,r}(k^{2/3}log k)} ⋅ n^{O_r(1)} in H-minor-free graphs.

Cite As Get BibTex

Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond. Kick the Cliques. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.IPEC.2024.13

Author Details

Gaétan Berthe
  • LIRMM, Université de Montpellier, CNRS, Montpellier, France
Marin Bougeret
  • LIRMM, Université de Montpellier, CNRS, Montpellier, France
Daniel Gonçalves
  • LIRMM, Université de Montpellier, CNRS, Montpellier, France
Jean-Florent Raymond
  • Univ. Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP UMR5668, Lyon, France

Funding

  • Raymond, Jean-Florent: Supported by the ANR project GRALMECO (ANR-21-CE48-0004).

References

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