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：本文针对加权相关性聚类问题提出了一种快速且简单的组合近似算法。在该问题中，我们有一个顶点集，每对顶点具有两个相异性权重值和相似性权重值，目标是以最小的总簇内相异性权重与簇间相似性权重之和对顶点进行聚类。当问题实例满足概率约束条件时，本算法的近似因子为3（已知最佳结果为5）。若实例在满足概率约束的同时还满足三角不等式，则近似因子为1.6（已知最佳结果为2）。