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International Workshop on Frontiers in Algorithmics

FAW 2018: Frontiers in Algorithmics pp 140–153Cite as

Kernelization for \(P_2\)-Packing: A Gerrymandering Approach

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10823))

Abstract

The \(P_2\)-packing problem asks for whether a graph contains k vertex-disjoint paths each of length two. We continue the study of its kernelization algorithms, and develop a 5k-vertex kernel.

Supported in part by NSFC under grant 61502054, RGC under grant PolyU 252026/15E, NSFC under grant 61572414, Natural Science Foundation of Hunan Province under grant 2017JJ3333 and Scientific Research Fund of Hunan Provincial Education Department under grant 17C0047.

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Notes

  1. 1.

    One may define the reducible set in a way that an edge component is regarded as two single-vertex components. This definition might reveal more reducible sets. However, it would slightly complicate our presentation without helping our analysis in the worst case, and hence we choose to use the simpler one.

  2. 2.

    Proofs of propositions marked with \(*\) are omitted due to space limit.

  3. 3.

    Actually, when neither \(U_1\) nor \(U_2\) is a (1, 4)-unit, we can move vertices in an arbitrary direction. We choose this way to simplify our proof.

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Authors and Affiliations

  1. Changsha University of Science and Technology, Changsha, China

    Wenjun Li

  2. Department of Computing, Hong Kong Polytechnic University, Hong Kong, China

    Junjie Ye & Yixin Cao

Authors
  1. Wenjun Li
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  2. Junjie Ye
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  3. Yixin Cao
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Corresponding author

Correspondence to Junjie Ye .

Editor information

Editors and Affiliations

  1. Texas A&M University, College Station, Texas, USA

    Jianer Chen

  2. Shanghai University of Finance and Economics, Shanghai, China

    Pinyan Lu

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Li, W., Ye, J., Cao, Y. (2018). Kernelization for \(P_2\)-Packing: A Gerrymandering Approach. In: Chen, J., Lu, P. (eds) Frontiers in Algorithmics. FAW 2018. Lecture Notes in Computer Science(), vol 10823. Springer, Cham. https://doi.org/10.1007/978-3-319-78455-7_11

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  • DOI: https://doi.org/10.1007/978-3-319-78455-7_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78454-0

  • Online ISBN: 978-3-319-78455-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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