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Approximation algorithms for the lower bounded correlation clustering problem

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Abstract

Lower bounded correlation clustering problem (LBCorCP) is a new generalization of the correlation clustering problem (CorCP). In the LBCorCP, we are given an integer L and a complete labelled graph. Each edge in the graph is either positive or negative based on the similarity of its two endpoints. The goal is to find a clustering of the vertices, each cluster contains at least L vertices, so as to minimize the sum of the number of positive cut edges and negative uncut edges. In this paper, we first introduce the LBCorCP and give three algorithms for this problem. The first algorithm is a random algorithm, which is designed for the instances of the LBCorCP with fewer positive edges. The second one is that we let the set V itself as a cluster and prove that the algorithm works well on two specially instances with fewer negative edges. The last one is an LP-rounding based iterative algorithm, which is also provided for the instances with fewer negative edges. The above three algorithms can quickly solve some special instances in polynomial time and obtain a smaller approximation ratio. In addition, we conduct simulations to evaluate the performance of our algorithms.

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Notes

  1. https://github.com/Junhaodada/Approximation-algorithms-for-the-lower-bounded-correlation-clustering-problem

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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 Office for Philosophy and Social Sciences (No. 20BGL259). The third author is supported by the NSERC (06446) and National Natural Science Foundation of China (Nos. 11771386, 11971349, 71771117). The fourth and the fifth authors are supported by National Natural Science Foundation of China (No. 11871081).

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Authors and Affiliations

  1. Institute of Mathematics, Hebei University of Technology, Tianjin, 300401, People’s Republic of China

    Sai Ji

  2. School of Public Administration, Hainan University, Haikou, 570228, Hainan, People’s Republic of China

    Yinhong Dong

  3. Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

    Donglei Du

  4. Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Dongzhao Wang & Dachuan Xu

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  1. Sai Ji
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  2. Yinhong Dong
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  3. Donglei Du
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  4. Dongzhao Wang
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  5. Dachuan Xu
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Correspondence to Dachuan Xu.

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A preliminary version of this paper appeared in Proceedings of the 10th International Conference on Computational Data and Social Networks, pp. 39–49, 2021.

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Ji, S., Dong, Y., Du, D. et al. Approximation algorithms for the lower bounded correlation clustering problem. J Comb Optim 45, 43 (2023). https://doi.org/10.1007/s10878-022-00976-6

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