This article introduces a quick and simple combinatorial approximation algorithm for the Weighted correlation clustering problem. In this problem, we have a set of vertices and two difference and similarity weight values for each pair of vertices, and the goal is to cluster the vertices with minimum total intra-cluster difference weights plus inter-cluster similarity weights. Our algorithm's approximation factor is 3 when an instance of this problem satisfies probability constraints (the best-known was 5). If the instance satisfies triangle inequality in addition to probability constraints, the approximation factor is 1.6 (the best-known was 2).

翻译：本文提出了一种快速简洁的组合近似算法，用于解决加权相关聚类问题。在该问题中，我们拥有一组顶点及每对顶点间的差异权重和相似权重，目标是对顶点进行聚类，使得簇内差异权重与簇间相似权重之和最小。当问题实例满足概率约束时，该算法的近似因子为3（此前最佳结果为5）；若实例在满足概率约束的同时还满足三角不等式，近似因子则为1.6（此前最佳结果为2）。