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A General Kernelization Technique for Domination and Independence Problems in Sparse Classes

Authors Carl Einarson, Felix Reidl



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Author Details

Carl Einarson
  • Royal Holloway, University of London, UK
Felix Reidl
  • Birkbeck, University of London, UK

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Carl Einarson and Felix Reidl. A General Kernelization Technique for Domination and Independence Problems in Sparse Classes. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 11:1-11:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.IPEC.2020.11

Abstract

We unify and extend previous kernelization techniques in sparse classes [Jochen Alber et al., 2004; Pilipczuk and Siebertz, 2018] by defining water lilies and show how they can be used in bounded expansion classes to construct linear bikernels for (r,c)-Dominating Set, (r,c)-Scattered Set, Total r-Domination, r-Roman Domination, and a problem we call (r,[λ,μ])-Domination (implying a bikernel for r-Perfect Code). At the cost of slightly changing the output graph class our bikernels can be turned into kernels. We also demonstrate how these constructions can be combined to create "multikernels", meaning graphs that represent kernels for multiple problems at once.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Dominating Set
  • Independence
  • Kernelization
  • Bounded Expansion

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References

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