(Meta) Kernelization

Abstract : In a parameterized problem, every instance I comes with a positive integer k. The problem is said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the instance I to a polynomial in k, while preserving the answer. In this work we give two meta-theorems on kernelzation. The first theorem says that all problems expressible in Counting Monadic Second Order Logic and satisfying a coverability property admit a polynomial kernel on graphs of bounded genus. Our second result is that all problems that have finite integer index and satisfy a weaker coverability property admit a linear kernel on graphs of bounded genus. These theorems unify and extend all previously known kernelization results for planar graph problems.
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Pré-publication, Document de travail
Complete version of the paper of FOCS 2009. 2013
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00904532
Contributeur : Dimitrios M. Thilikos <>
Soumis le : jeudi 14 novembre 2013 - 16:13:13
Dernière modification le : vendredi 5 octobre 2018 - 21:14:01

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  • HAL Id : lirmm-00904532, version 1
  • ARXIV : 0904.0727

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Hans L. Bodlaender, Fedor V. Fomin, Daniel Lokshtanov, Eelko Penninkx, Saket Saurabh, et al.. (Meta) Kernelization. Complete version of the paper of FOCS 2009. 2013. 〈lirmm-00904532〉

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