Summary: Kernelization – a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems – plays a central role in parameterized complexity and has triggered an extensive line of research. In this paper we consider a restricted yet natural variant of kernelization, namely strict kernelization, where one is not allowed to increase the parameter of the reduced instance (the kernel) by more than an additive constant. Building on earlier work of Y. Chen et al. [Theory Comput. Syst. 48, No. 4, 803–839 (2011; Zbl 1234.68118)], we underline the applicability of their framework by showing that a variety of fixed-parameter tractable problems, including graph problems and Turing machine computation problems, does not admit strict polynomial kernels under the weaker assumption of \(\mathrm{P}\neq \mathrm{NP}\). Finally, we study a relaxation of the notion of strict kernels.
For the entire collection see [Zbl 1391.68009].