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CORR
2010
Springer

Cross-Composition: A New Technique for Kernelization Lower Bounds

10 years 8 months ago
Cross-Composition: A New Technique for Kernelization Lower Bounds
We introduce a new technique for proving kernelization lower bounds, called cross-composition. A classical problem L cross-composes into a parameterized problem Q if an instance of Q with polynomially bounded parameter value can express the logical OR of a sequence of instances of L. Building on work by Bodlaender et al. (ICALP 2008) and using a result by Fortnow and Santhanam (STOC 2008) we show that if an NP-hard problem cross-composes into a parameterized problem Q then Q does not admit a polynomial kernel unless the polynomial hierarchy collapses. Our technique generalizes and strengthens the recent techniques of using or-composition algorithms and of transferring the lower bounds via polynomial parameter transformations. We show its applicability by proving kernelization lower bounds for a number of important graphs problems with structural (non-standard) parameterizations, e.g., Chromatic Number, Clique, and Weighted Feedback Vertex Set do not admit polynomial kernels with respe...
Hans L. Bodlaender, Bart M. P. Jansen, Stefan Krat
Added 22 Mar 2011
Updated 22 Mar 2011
Type Journal
Year 2010
Where CORR
Authors Hans L. Bodlaender, Bart M. P. Jansen, Stefan Kratsch
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