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Linear Problem Kernels for Planar Graph Problems with Small Distance Property

  • Jianxin Wang
  • Yongjie Yang
  • Jiong Guo
  • Jianer Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6907)

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.

Keywords

Planar Graph Vertex Cover Linear Kernel Kernel Size Reduction Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2011

Authors and Affiliations

  • Jianxin Wang
    • 1
  • Yongjie Yang
    • 1
  • Jiong Guo
    • 2
  • Jianer Chen
    • 3
  1. 1.School of Information Science and EngineeringCentral South UniversityChangshaP.R. China
  2. 2.Universität des SaarlandesSaarbrückenGermany
  3. 3.Department of Computer Science and EngineeringTexas A&M UniversityUSA

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