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arXiv · 0904.0727

(Meta) Kernelization

Hans L. Bodlaender·Fedor V. Fomin·Daniel Lokshtanov·Eelko Penninkx·Saket Saurabh·Dimitrios M. Thilikos
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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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Hans L. Bodlaender, Fedor V. Fomin, Daniel Lokshtanov, Eelko Penninkx, Saket Saurabh, Dimitrios M. Thilikos. 2013-09-25. (Meta) Kernelization. https://arxiv.org/abs/0904.0727

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