(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.
Cite
@article{arxiv.0904.0727,
title = {(Meta) Kernelization},
author = {Hans L. Bodlaender and Fedor V. Fomin and Daniel Lokshtanov and Eelko Penninkx and Saket Saurabh and Dimitrios M. Thilikos},
journal= {arXiv preprint arXiv:0904.0727},
year = {2013}
}
Comments
Complete version of the paper of FOCS 2009