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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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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