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Preprints, Working Papers, ... Year : 2013

(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.

Dates and versions

lirmm-00904532 , version 1 (14-11-2013)

Identifiers

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

Cite

Hans L. Bodlaender, Fedor V. Fomin, Daniel Lokshtanov, Eelko Penninkx, Saket Saurabh, et al.. (Meta) Kernelization. 2013. ⟨lirmm-00904532⟩
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