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Approximation Algorithm for the Balanced 2-correlation Clustering Problem on Well-Proportional Graphs

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Algorithmic Aspects in Information and Management (AAIM 2020)

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Abstract

In this paper, we consider the balanced 2-correlation clustering problem on well-proportional graphs, which has applications in protein interaction networks, cross-lingual link detection, communication networks, among many others. Given a complete graph \(G=(V,E)\) with each edge \((u,v)\in E\) labeled by \(+\) or −, the goal is to partition the vertices into two clusters of equal size to minimize the number of positive edges whose endpoints lie in different clusters plus the number of negative edges whose endpoints lie in the same cluster. We provide a \((3,\max \{4(M+1),16\})\)-balanced approximation algorithm for the balanced 2-correlation clustering problem on M-proportional graphs. Namely, the cost of the vertex partition \(\{V_1, V_2\}\) returned by the algorithm is at most \(\max \{4(M+1),16\}\) times the optimum solution, and \(\min \{|V_1|,|V_2|\} \le 3\max \{|V_1|\), \( |V_2|\}\).

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Acknowledgements

The first two authors are supported by National Natural Science Foundation of China (Nos. 11531014, 11871081). The third author is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant 06446, and National Natural Science Foundation of China (Nos. 11771386, 11728104). The fourth author is supported by National Natural Science Foundation of China (No. 11201333).

Author information

Authors and Affiliations

  1. Department of Operations Research and Information Engineering, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Sai Ji & Dachuan Xu

  2. Faculty of Management, University of New Brunswick, Fredericton, NB, E3B 9Y2, Canada

    Donglei Du

  3. Glorious Sun School of Business and Management, Donghua University, Shanghai, 200051, People’s Republic of China

    Ling Gai

Authors
  1. Sai Ji
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  2. Dachuan Xu
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  3. Donglei Du
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  4. Ling Gai
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Corresponding author

Correspondence to Ling Gai .

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Editors and Affiliations

  1. Zhejiang Normal University, Jinhua, China

    Zhao Zhang

  2. Texas Southern University, Houston, TX, USA

    Wei Li

  3. University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

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Ji, S., Xu, D., Du, D., Gai, L. (2020). Approximation Algorithm for the Balanced 2-correlation Clustering Problem on Well-Proportional Graphs. In: Zhang, Z., Li, W., Du, DZ. (eds) Algorithmic Aspects in Information and Management. AAIM 2020. Lecture Notes in Computer Science(), vol 12290. Springer, Cham. https://doi.org/10.1007/978-3-030-57602-8_9

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  • DOI: https://doi.org/10.1007/978-3-030-57602-8_9

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  • Print ISBN: 978-3-030-57601-1

  • Online ISBN: 978-3-030-57602-8

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