Abstract
Correlation clustering problem is a classical clustering problem and has many applications in protein interaction networks, cross-lingual link detection, communication networks, etc. In this paper, we discuss the capacitated correlation clustering problem on labeled complete graphs, in which each edge is labeled \(+\) or − to indicate two endpoints are “similar" or “dissimilar", respectively. Our objective is to partition the vertex set into several clusters, subject to an upper bound on cluster size, so as to minimize the number of disagreements. Here the number of disagreements is defined as the total number of the edges with positive labels between clusters and the edges with negative labels within clusters. The main contribution of this work is providing a 5.37-approximation algorithm for the capacitated correlation clustering problem, improving the current best approximation ratio of 6 [21]. In addition, we have conducted a series of numerical experiments, which effectively demonstrate the effectiveness of our algorithm.
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Acknowledgements
The first author is supported by National Natural Science Foundation of China (No. 12101594) and the Project funded by China Postdoctoral Science Foundation (No. 2021M693337). The second author is supported by National Nature Science Foundation of China (No. 11871366), Qing Lan Project for Young Academic Leaders and Qing Lan Project for Key Teacher. The third author is supported by Natural Science Foundation of Shandong Province (No. ZR2017LA002). The fourth author is supported by National Natural Science Foundation of China (No. 12131003) and Beijing Natural Science Foundation Project No. Z200002.
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Ji, S., Cheng, Y., Tan, J., Zhao, Z. (2021). An Improved Approximation Algorithm for Capacitated Correlation Clustering Problem. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_4
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