Correlation clustering problem is a clustering problem which has many applications such as protein interaction networks, cross-lingual link detection, communication networks, and social computing. In this paper, we introduce two variants of correlation clustering problem: correlation clustering problem on uncertain graphs and correlation clustering problem with non-uniform hard constrained cluster sizes. Both problems overcome part of the limitations of the existing variants of correlation clustering problem and have practical applications in the real world. We provide a constant approximation algorithm and two approximation algorithms for the former and the latter problem, respectively.

相关聚类问题是一种聚类问题，它具有许多应用，例如蛋白质相互作用网络，跨语言链接检测，通信网络和社交计算。在本文中，我们介绍了相关性聚类问题的两个变体：不确定图上的相关性聚类问题和具有非均匀硬约束聚类大小的相关性聚类问题。这两个问题都克服了相关性聚类问题现有变体的部分局限性，并在现实世界中具有实际应用。对于前一个问题和后一个问题，我们分别提供了一个常数近似算法和两个近似算法。