Improved linear problem kernel for planar connected dominating set

Authors:
Weizhong Luo;Jianxin Wang;Qilong Feng;Jiong Guo;Jianer Chen
Affiliations:
-;-;-;-;-
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

In this paper, we study the Planar Connected Dominating Set problem, which, given a planar graph G=(V,E) and a non-negative integer k, asks for a subset D@?V with |D|@?k such that D forms a dominating set of G and induces a connected graph. Answering an open question posed at the 2nd Workshop on Kernelization (WorKer 2010), we provide a kernelization algorithm for this problem, leading to a problem kernel with at most 130k vertices, improving the previously best upper bound on the kernel size. To this end, we incorporate a vertex coloring technique with data reduction rules and introduce a type distinction of regions into the region decomposition framework, which allows a refined analysis of the region size.