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Approximation algorithms for the lower bounded correlation clustering problem

Author

Listed:
  • Sai Ji

    (Hebei University of Technology)

  • Yinhong Dong

    (Hainan University)

  • Donglei Du

    (University of New Brunswick)

  • Dongzhao Wang

    (Beijing University of Technology)

  • Dachuan Xu

    (Beijing University of Technology)

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.

Suggested Citation

  • Sai Ji & Yinhong Dong & Donglei Du & Dongzhao Wang & Dachuan Xu, 2023. "Approximation algorithms for the lower bounded correlation clustering problem," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-19, January.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00976-6
    DOI: 10.1007/s10878-022-00976-6
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    References listed on IDEAS

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    1. Takuro Fukunaga, 2019. "LP-based pivoting algorithm for higher-order correlation clustering," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1312-1326, May.
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