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On Editing Graphs into 2-Club Clusters

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Frontiers in Algorithmics and Algorithmic Aspects in Information and Management

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

Abstract

In this paper, we introduce and study three graph modification problems: 2-Club Cluster Vertex Deletion, 2-Club Cluster Edge Deletion, and 2-Club Cluster Editing. In 2-Club Cluster Vertex Deletion (2-Club Cluster Edge Deletion, and 2-Club Cluster Editing), one is given an undirected graph G and an integer k ≥ 0, and needs to decide whether it is possible to transform G into a 2-club cluster graph by deleting at most k vertices (by deleting at most k edges, and by deleting and adding totally at most k edges). Here, a 2-club cluster graph is a graph in which every connected component is of diameter 2. We first prove that all these three problems are NP-complete. Then, we present for 2-Club Cluster Vertex Deletion a fixed parameter algorithm with running time O  ∗ (3.31k), and for 2-Club Cluster Edge Deletion a fixed parameter algorithm with running time O  ∗ (2.74k).

Research supported by the National Natural Science Foundation of China (61070019) and the National Natural Science Foundation of China (60603007).

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Author information

Authors and Affiliations

  1. School of Computer Science and Technology, Shandong University, Shandong, China

    Hong Liu, Peng Zhang & Daming Zhu

  2. Provincial Key Laboratory of Software Engineering, Jinan, China

    Hong Liu, Peng Zhang & Daming Zhu

Authors
  1. Hong Liu
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  2. Peng Zhang
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  3. Daming Zhu
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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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Liu, H., Zhang, P., Zhu, D. (2012). On Editing Graphs into 2-Club Clusters. 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_22

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  • DOI: https://doi.org/10.1007/978-3-642-29700-7_22

  • 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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