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

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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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References

  1. Achtert, E., B\(\ddot{\rm o}\)hm, C., David, J., Kr\(\ddot{\rm o}\)ger, P., Zimek, A.: Global correlation clustering based on the Hough transform. Stat. Anal. Data Mining 1, 111–127 (2010)

    Google Scholar 

  2. Ahmadian, S., Norouzi-Fard, A., Svensson, O., Ward, J.: Better guarantees for \(k\)-means and Euclidean \(k\)-median by primal-dual algorithms. In: Proceedings of FOCS, pp. 61–72 (2017)

    Google Scholar 

  3. Ahn, K.J., Cormode, G., Guha, S., Mcgregor, A., Wirth, A.: Correlation clustering in data streams. In: Proceedings of ICML, pp. 2237–2246 (2015)

    Google Scholar 

  4. Ailon, N., Avigdor-Elgrabli, N., Liberty, E., Zuylen, A.V.: Improved approximation algorithms for bipartite correlation clustering. SIAM J. Comput. 41, 1110–1121 (2012)

    Article  MathSciNet  Google Scholar 

  5. Ailon, N., Charikar, M., Newman, A.: Aggregating inconsistent information: ranking and clustering. J. ACM 55(5) (2008). Article No. 23

    Google Scholar 

  6. Amit, N.: The bicluster graph editing problem. Diss, Tel Aviv University (2004)

    Google Scholar 

  7. Arthur, D., Vassilvitskii, S.: \(k\)-Means++: the advantages of careful seeding. In: Proceedings of SODA, pp. 1027–1035 (2007)

    Google Scholar 

  8. Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Mach. Learn. 56, 89–113 (2004)

    Article  MathSciNet  Google Scholar 

  9. Behsaz, B., Friggstad, Z., Salavatipour, M.R., Sivakumar, R.: Approximation algorithms for min-sum k-clustering and balanced k-median. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9134, pp. 116–128. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47672-7_10

    Chapter  MATH  Google Scholar 

  10. Bonchi, F.: Overlapping correlation clustering. Knowl. Inf. Syst. 35, 1–32 (2013)

    Google Scholar 

  11. Braverman, V., Lang, H., Levin, K., Monemizadeh, M.: Clustering problems on sliding windows. In: Proceedings of SODA, pp. 1374–1390 (2016)

    Google Scholar 

  12. Byrka, J., Fleszar, K., Rybicki, B., Spoerhase, J.: Bi-factor approximation algorithms for hard capacitated \(k\)-median problems. In: Proceedings of SODA, pp. 722–736 (2015)

    Google Scholar 

  13. Charikar, M., Guruswami, V., Wirth, A.: Clustering with qualitative information. J. Comput. Syst. Sci. 71, 360–383 (2005)

    Article  MathSciNet  Google Scholar 

  14. Chawla, S., Makarychev, K., Schramm, T., Yaroslavtsev, G.: Near optimal LP rounding algorithm for correlation clustering on complete and complete \(k\)-partite graphs. In: Proceedings of STOC, pp. 219–228 (2015)

    Google Scholar 

  15. Demaine, E., Emanuel, D., Fiat, A., Immorlica, N.: Correlation clustering in general weighted graphs. Theoret. Comput. Sci. 361, 172–187 (2006)

    Article  MathSciNet  Google Scholar 

  16. Frieze, A., Jerrum, M.: Improved approximation algorithms for max \(k\)-cut and max bisection. Algorithmica 18, 67–81 (1997)

    Article  MathSciNet  Google Scholar 

  17. Giotis, I., Guruswami, V.: Correlation clustering with a fixed number of clusters. In: Proceedings of SODA, pp. 1167–1176 (2006)

    Google Scholar 

  18. Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42, 1115–1145 (1995)

    Article  MathSciNet  Google Scholar 

  19. Hendrickx, J.M., Tsitsiklis, J.N.: Convergence of type-symmetric and cut-balanced consensus seeking systems. IEEE Trans. Autom. Control 58, 214–218 (2013)

    Article  MathSciNet  Google Scholar 

  20. Ji, S., Xu, D., Li, M., Wang, Y.: Approximation algorithm for the correlation clustering problem with non-uniform hard constrained cluster sizes. In: Du, D.-Z., Li, L., Sun, X., Zhang, J. (eds.) AAIM 2019. LNCS, vol. 11640, pp. 159–168. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-27195-4_15

    Chapter  Google Scholar 

  21. Kuila, P., Jana, P.K.: Approximation schemes for load balanced clustering in wireless sensor networks. J. Supercomput. 68(1), 87–105 (2013). https://doi.org/10.1007/s11227-013-1024-6

    Article  Google Scholar 

  22. Li, S.: On uniform capacitated \(k\)-median beyond the natural LP relaxation. ACM Trans. Algorithms 13(2) (2017). Article No. 22

    Google Scholar 

  23. Li, M., Xu, D., Zhang, D., Zhang, T.: A streaming algorithm for \(k\)-means with approximate coreset. Asia Pacific J. Oper. Res. 36(01), 1950006 (2019)

    Article  MathSciNet  Google Scholar 

  24. Liao, Y., Qi, H., Li, W.: Load-balanced clustering algorithm with distributed self-organization for wireless sensor networks. IEEE Sens. J. 13, 1498–1506 (2013)

    Article  Google Scholar 

  25. Mathieu, C., Sankur, O., Schudy, W.: Online correlation clustering. Comput. Stat. 21, 211–229 (2010)

    MATH  Google Scholar 

  26. Mathieu, C., Schudy, W.: Correlation clustering with noisy input. In: Proceedings of SODA, pp. 712–728 (2010)

    Google Scholar 

  27. Puleo, G.J., Milenkovic, O.: Correlation clustering with constrained cluster sizes and extended weights bounds. SIAM J. Optim. 25, 1857–1872 (2015)

    Article  MathSciNet  Google Scholar 

  28. Puleo, G.J., Milenkovic, O.: Correlation clustering and biclustering with locally bounded errors. IEEE Trans. Inf. Theory 64, 4105–4119 (2018)

    Article  MathSciNet  Google Scholar 

  29. Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. Discrete Appl. Math. 144, 173–182 (2004)

    Article  MathSciNet  Google Scholar 

  30. Swamy, C.: Correlation clustering: maximizing agreements via semidefinite programming. In: Proceedings of SODA, pp. 526–527 (2004)

    Google Scholar 

  31. Zhao, M., Yang, Y., Wang, C.: Mobile data gathering with load balanced clustering and dual data uploading in wireless sensor networks. IEEE Trans. Mob. Comput. 14, 770–785 (2015)

    Article  Google Scholar 

Download references

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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-57601-1

  • Online ISBN: 978-3-030-57602-8

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