Kernelization using structural parameters on sparse graph classes

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Authors	GAJARSKÝ Jakub HLINĚNÝ Petr OBDRŽÁLEK Jan ORDYNIAK Sebastian REIDL Felix ROSSMANITH Peter VILLAAMIL Fernando SIKDAR Somnath
Year of publication	2017
Type	Article in Periodical
Magazine / Source	Journal of Computer and System Sciences
MU Faculty or unit	Faculty of Informatics
Citation
Doi	http://dx.doi.org/10.1016/j.jcss.2016.09.002
Field	Informatics
Keywords	Parameterized complexity; Kernelization; Nowhere dense graphs; Finite integer index; Treedepth
Description	We prove that graph problems with finite integer index have linear kernels on graphs of bounded expansion when parameterized by the size of a modulator to constant-treedepth graphs. For nowhere dense graph classes, our result yields almost-linear kernels. We also argue that such a linear kernelization result with a weaker parameter would fail to include some of the problems covered by our framework. We only require the problems to have FII on graphs of constant treedepth. This allows to prove linear kernels also for problems such as Longest-Path/Cycle, Exact-s, t-Path, Treewidth, and Pathwidth, which do not have FII on general graphs. (C) 2016 Elsevier Inc. All rights reserved.
Related projects:	Parametrizované algoritmy a kernelizace v kontextu diskrétní matematiky a logiky Rozsáhlé výpočetní systémy: modely, aplikace a verifikace V.