Kernels for packing and covering problems

  • Authors:

  • Jianer Chen;Henning Fernau;Peter Shaw;Jianxin Wang;Zhibiao Yang

  • Affiliations:

  • School of Information Science and Engineering, Central South University, Changsha, P.R. China,Department of Computer Science and Engineering, Texas A&M University, College Station, Texas;FB IV--Abteilung Informatik, Universität Trier, Trier, Germany;School of Engineering and Information Technology, Charles Darwin University, Darwin, Northern Territory, Australia;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

  • Venue:
  • FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2012

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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.