Parametric duality and kernelization: lower bounds and upper bounds on kernel size

Authors:
Jianer Chen;Henning Fernau;Iyad A. Kanj;Ge Xia
Affiliations:
Department of Computer Science, Texas A&M University, College Station, TX;The University of Newcastle, School of Electrical Engineering and Computer Science, (Universität Tübingen, Wilhelm-Schickard-Institut für Informatik, Sand 13, D-72076 Tübingen, ...;School of Computer Science, Telecommunications and Information Systems, DePaul University, Chicago, IL;Department of Computer Science, Texas A&M University, College Station, TX
Venue:
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Year:
2005

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Abstract

We develop new techniques to derive lower bounds on the kernel size for certain parameterized problems. For example, we show that unless $\mathcal{P}$=$\mathcal{NP}$, planar vertex cover does not have a problem kernel of size smaller than 4k/3, and planar independent set and planar dominating set do not have kernels of size smaller than 2k. We derive an upper bound of 67k on the problem kernel for planar dominating set improving the previous 335k upper bound by Alber et al.