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Improved Approximation Algorithm for Minimum Weight k-Subgraph Cover Problem

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Combinatorial Optimization and Applications (COCOA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11949))

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Abstract

For a graph G, a vertex subset C is a Connected k-Subgraph Cover (VCC\(_k\)) if every connected subgraph on k vertices of G contains at least one vertex from C. Using local ratio method, a \((k-1)\)-approximation algorithm was given in [14] for the minimum weight VCC\(_k\) problem under the assumption that the girth g(G) (the length of a shortest cycle of G) is at least k. In this paper, we prove that a \((k-1)\)-approximation can be achieved when \(k\ge 5\) and \(g(G)>2k/3\). Although our algorithm also employs the local ratio method, the analysis has a big difference from that in [14], this is why the girth constraint can be relaxed from k to 2k/3.

This research work is supported in part by NSFC (11771013, 11531011, 61751303), and ZJNSFC (LD19A010001, LY19A010018).

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Pengcheng Liu & Zhao Zhang

  2. Library and Information Center, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Xiaohui Huang

Authors
  1. Pengcheng Liu
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  2. Xiaohui Huang
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  3. Zhao Zhang
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Correspondence to Zhao Zhang .

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Editors and Affiliations

  1. Georgia State University, Atlanta, GA, USA

    Yingshu Li

  2. Florida Atlantic University, Boca Raton, FL, USA

    Mihaela Cardei

  3. Kennesaw State University, Marietta, GA, USA

    Yan Huang

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Liu, P., Huang, X., Zhang, Z. (2019). Improved Approximation Algorithm for Minimum Weight k-Subgraph Cover Problem. In: Li, Y., Cardei, M., Huang, Y. (eds) Combinatorial Optimization and Applications. COCOA 2019. Lecture Notes in Computer Science(), vol 11949. Springer, Cham. https://doi.org/10.1007/978-3-030-36412-0_28

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  • DOI: https://doi.org/10.1007/978-3-030-36412-0_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-36411-3

  • Online ISBN: 978-3-030-36412-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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