An improved kernel for planar connected dominating set

  • Authors:

  • Weizhong Luo;Jianxin Wang;Qilong Feng;Jiong Guo;Jianer Chen

  • Affiliations:

  • School of Information Science and Engineering, Central South University, Changsha, P.R. China and Hunan Financial & Economic University, Changsha, P.R. China;School of Information Science and Engineering, Central South University, Changsha, P.R. China;School of Information Science and Engineering, Central South University, Changsha, P.R. China;Universität des Saarlandes, Saarbrücken, Germany;School of Information Science and Engineering, Central South University, Changsha, P.R. China and Department of Computer Science and Engineering, Texas A&M University, College Station, Texas

  • Venue:
  • TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
  • Year:
  • 2011

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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 by S. Saurabh [The 2nd Workshop on Kernelization (WorKer 2010)], we provide a kernelization algorithm for this problem leading to a problem kernel with 130k vertices, significantly 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 for the first time a distinction of two types of regions into the region decomposition framework, which allows a refined analysis of the region size and could be used to reduce the kernel sizes achieved by the region decomposition technique for a large range of problems.