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Frontiers in Algorithmics and Algorithmic Aspects in Information and Management pp 199–211Cite as

Kernels for Packing and Covering Problems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7285))

Abstract

We show how the notion of combinatorial duality, related to the well-known notion of duality from linear programming, may be used for translating kernel results obtained for packing problems into kernel results for covering problems. We exemplify this approach by having a closer look at the problems of packing a graph with vertex-disjoint trees with r edges. We also improve on the best known kernel size for packing graphs with trees containing two edges, which has been well studied.

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Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, 410083, P.R. China

    Jianer Chen, Jianxin Wang & Zhibiao Yang

  2. Department of Computer Science and Engineering, Texas A&M University, College Station, Texas, 77843-3112, USA

    Jianer Chen

  3. FB IV—Abteilung Informatik, Universität Trier, D-54286, Trier, Germany

    Henning Fernau

  4. School of Engineering and Information Technology, Charles Darwin University, Darwin, Northern Territory, Australia, 0909

    Peter Shaw

Authors
  1. Jianer Chen
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  2. Henning Fernau
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  3. Peter Shaw
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  4. Jianxin Wang
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  5. Zhibiao Yang
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of North Carolina, CB 3175 Brooks Bldg, 27599-3175, Chapel Hill, NC, USA

    Jack Snoeyink

  2. Microsoft Research Asia, No 999, Zixing Road, Minhang District, 200241, Shanghai, China

    Pinyan Lu

  3. Peking University, Science BLK 1, No.5 Yiheyuan Road, Haidian District, 100871, Beijing, P.R.China

    Kaile Su

  4. Department of Computer Science, City University of Hong Kong, Tat Chee Ave., Kowloon, Hong Kong

    Lusheng Wang

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© 2012 Springer-Verlag Berlin Heidelberg

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Chen, J., Fernau, H., Shaw, P., Wang, J., Yang, Z. (2012). Kernels for Packing and Covering Problems. In: Snoeyink, J., Lu, P., Su, K., Wang, L. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29700-7_19

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  • DOI: https://doi.org/10.1007/978-3-642-29700-7_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29699-4

  • Online ISBN: 978-3-642-29700-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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