Abstract
This paper considers the correlation clustering problem with non-uniform hard constrained cluster sizes, which is a generalization of correlation clustering problem. In this problem, we are given a positive integer \(U_v\) for each vertex v, and require \(|C|\le \min _{v\in C}U_v\) for any cluster C. We provide a (2, 4)-bicriteria approximation algorithm for this problem. Namely, the solution returned by the algorithm has the cost that is at most 4 times the optimum, and for each cluster C in the solution, we have \(|C|\le 2\min _{v\in C}U_v\).
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References
Amit, N.: The bicluster graph editing problem. Diss, Tel Aviv University (2004)
Ailon, N., Avigdor-Elgrabli, N., Liberty, E., Zuylen, A.V.: Improved approximation algorithms for bipartite correlation clustering. SIAM J. Comput. 41(5), 1110–1121 (2012)
Achtert, E., B\(\ddot{o}\)hm, C., David, J., Kr\(\ddot{o}\)ger, P., Zimek, A.: Global correlation clustering based on the hough transform. Stat. Anal. Data Min. 1(3), 111–127 (2010)
Ahn, K.J., Cormode, G., Guha, S., Mcgregor, A., Wirth, A.: Correlation clustering in data streams. In: Proceedings of the 32th International Conference on International Conference on Machine Learning (ICML), pp. 2237–2246 (2015)
Ailon, N., Charikar, M., Newman, A.: Aggregating inconsistent information: ranking and clustering. J. ACM, 55(5), Article No. 23 (2008)
Arthur, D., Vassilvitskii, S.: k-Means++: the advantages of careful seeding. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1027–1035 (2007)
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 the 58th Annual Symposium on Foundations of Computer Science (FOCS), pp. 61–72 (2017)
Bonchi, F.: Overlapping correlation clustering. Knowl. Inf. Syst. 35(1), 1–32 (2013)
Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Mach. Learn. 56(1–3), 89–113 (2004)
Byrka, J., Fleszar, K., Rybicki, B., Spoerhase, J.: Bi-factor approximation algorithms for hard capacitated \(k\)-median problems. In: Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 722–736 (2015)
Braverman, V., Lang, H., Levin, K., Monemizadeh, M.: Clustering problems on sliding windows. In: Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1374–1390 (2016)
Charikar, M., Guruswami, V., Wirth, A.: Clustering with qualitative information. J. Comput. Syst. Sci. 71(3), 360–383 (2005)
Chawla, S., Makarychev, K., Schramm, T., Yaroslavtsev, G.: Near optimal LP rounding algorithm for correlationclustering on complete and complete k-partite graphs. In: Proceedings of the 47th Annual ACM Symposium on Theory of Computing (STOC), pp. 219–228 (2015)
Demaine, E., Emanuel, D., Fiat, A., Immorlica, N.: Correlation clustering in general weighted graphs. Theoret. Comput. Sci. 361(2), 172–187 (2006)
Frieze, A., Jerrum, M.: Improved approximation algorithms for maxk-cut and max bisection. Algorithmica 18(1), 67–81 (1997)
Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. ACM 42(6), 1115–1145 (1995)
Giotis, I., Guruswami, V.: Correlation clustering with a fixed number of clusters. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1167–1176 (2006)
Li, S.: On uniform capacitated \(k\)-median beyond the natural LP relaxation. ACM Trans. Algorithms, 13(2), Article No. 22 (2017)
Li, M., Xu, D., Zhang, D., Zhang, T.: A streaming algorithm for k-means with approximate coreset. Asia Pac. J. Oper. Res. 36, 1–18 (2019)
Mathieu, C., Schudy, W.: Correlation clustering with noisy input. In: Proceedings of the 21th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 712–728 (2010)
Mathieu, C., Sankur, O., Schudy, W.: Online correlation clustering. Comput. Stat. 21(2), 211–229 (2010)
Puleo, G.J., Milenkovic, O.: Correlation clustering with constrained cluster sizes and extended weights bounds. SIAM J. Optim. 25(3), 1857–1872 (2015)
Puleo, G.J., Milenkovic, O.: Correlation clustering and biclustering with locally bounded errors. IEEE Trans. Inf. Theory 64(6), 4105–4119 (2018)
Swamy, C.: Correlation clustering: maximizing agreements via semidefinite programming. In: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 526–527 (2004)
Acknowledgements
The second author is supported by National Natural Science Foundation of China (No. 11531014). The third author is supported by Higher Educational Science and Technology Program of Shandong Province (No. J17KA171). The forth author is supported by Natural Science Foundation of China (No. 61433012), Shenzhen Research Grant (KQJSCX2018033017 0311901, JCYJ20180305180840138 and GGFW201707311403 1767), and Shenzhen Discipline Construction Project for Urban Computing and Data Intelligence.
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Ji, S., Xu, D., Li, M., Wang, Y. (2019). Approximation Algorithm for the Correlation Clustering Problem with Non-uniform Hard Constrained Cluster Sizes. In: Du, DZ., Li, L., Sun, X., Zhang, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2019. Lecture Notes in Computer Science(), vol 11640. Springer, Cham. https://doi.org/10.1007/978-3-030-27195-4_15
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