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Polynomial Kernelizations For MIN F+Pi1 And MAX NP

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Kratsch,  Stefan
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Kratsch, S. (2009). Polynomial Kernelizations For MIN F+Pi1 And MAX NP. In S. Albers, & J.-Y. Marion (Eds.), 26th International Symposium on Theoretical Aspects of Computer Science. Wadern: Schloss Dagstuhl.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-18B7-F
Abstract
The relation of constant-factor approximability to fixed-parameter tractability and kernelization is a long-standing open question. We prove that two large classes of constant-factor approximable problems, namely~$\textsc{MIN F}^+\Pi_1$ and~$\textsc{MAX NP}$, including the well-known subclass~$\textsc{MAX SNP}$, admit polynomial kernelizations for their natural decision versions. This extends results of Cai and Chen (JCSS 1997), stating that the standard parameterizations of problems in~$\textsc{MAX SNP}$ and~$\textsc{MIN F}^+\Pi_1$ are fixed-parameter tractable, and complements recent research on problems that do not admit polynomial kernelizations (Bodlaender et al.\ ICALP 2008).