Bidimensionality and kernels

Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, Dimitrios M. Thilikos

Research output: Contribution to journalArticlepeer-review


Bidimensionality theory was introduced by [E. D. Demaine et al., J. ACM, 52 (2005), pp. 866-893] as a tool to obtain subexponential time parameterized algorithms on H-minor-free graphs. In [E. D. Demaine and M. Hajiaghayi, Bidimensionality: New connections between FPT algorithms and PTASs, in Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM, Philadelphia, 2005, pp. 590-601] this theory was extended in order to obtain polynomial time approximation schemes (PTASs) for bidimensional problems. In this work, we establish a third meta-algorithmic direction for bidimensionality theory by relating it to the existence of linear kernels for parameterized problems. In particular, we prove that every minor (resp., contraction) bidimensional problem that satisfies a separation property and is expressible in Countable Monadic Second Order Logic (CMSO) admits a linear kernel for classes of graphs that exclude a fixed graph (resp., an apex graph) H as a minor. Our results imply that a multitude of bidimensional problems admit linear kernels on the corresponding graph classes. For most of these problems no polynomial kernels on H-minor-free graphs were known prior to our work.

Original languageEnglish (US)
Pages (from-to)1397-1422
Number of pages26
JournalSIAM Journal on Computing
Issue number6
StatePublished - Dec 18 2020


  • Bidimensionality
  • Kernelization
  • Parameterized algorithms
  • Treewidth

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


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