Connectivity is not a limit for kernelization: planar connected dominating set

Authors:
Qianping Gu;Navid Imani
Affiliations:
School of Computing Science, Simon Fraser University, Burnaby, BC, Canada;School of Computing Science, Simon Fraser University, Burnaby, BC, Canada
Venue:
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Year:
2010

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Abstract

We prove a small linear-size kernel for the connected dominating set problem in planar graphs through data reduction. Our set of rules efficiently reduce a planar graph G with n vertices and connected dominating number γc(G) to a kernel of size at most 413γc(G) in O(n3) time answering the question of whether the connectivity criteria hinders the construction of small kernels, negatively (in case of the planar connected dominating set). Our result gives a fixed-parameter algorithm of time $(2^{O(\sqrt{\gamma_c(G)})}\cdot \gamma_c(G) + n^3)$ using the standard branch-decomposition based approach.