Linear problem kernels for planar graph problems with small distance property

  • Authors:

  • Jianxin Wang;Yongjie Yang;Jiong Guo;Jianer Chen

  • Affiliations:

  • 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;Department of Computer Science and Engineering, Texas A&M University, College Station, Texas

  • Venue:
  • MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
  • Year:
  • 2011

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Abstract

Recently, various linear problem kernels for NP-hard planar graph problems have been achieved, finally resulting in a meta-theorem for classification of problems admitting linear kernels. Almost all of these results are based on a so-called region decomposition technique. In this paper, we introduce a simple partition of the vertex set to analyze kernels for planar graph problems which admit the distance property with small constants. Without introducing new reduction rules, this vertex partition directly leads to improved kernel sizes for several problems. Moreover, we derive new kernelization algorithms for Connected Vertex Cover, Edge Dominating Set, and Maximum Triangle Packing problems, further improving the kernel size upper bounds for these problems.