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 weight values for each pair of vertices denoting their difference and similarity. The goal is to cluster the vertices with minimum total intra-cluster difference weights plus inter-cluster similarity weights. Our algorithm is a randomized approximation algorithm with $O(n^2)$ running time where $n$ is the number of vertices. Its approximation factor is 3 when the instance satisfies probability constraints. If the instance satisfies triangle inequality in addition to probability constraints, the approximation factor is 1.6. Both algorithms are superior to the best known results in terms of running time and the second one is also superior in terms of the approximation factor.

翻译：本文针对加权相关聚类问题提出了一种快速、简单的组合近似算法。在该问题中，我们有一个顶点集合，且每对顶点对应两个权重值，分别表示它们的相异度和相似度。目标是通过最小化簇内相异度权重与簇间相似度权重的总和来对顶点进行聚类。我们的算法是一种随机近似算法，其时间复杂度为$O(n^2)$，其中$n$为顶点数量。当问题实例满足概率约束时，其近似比为3。若实例在满足概率约束的同时还满足三角不等式，则近似比可提升至1.6。两种算法在时间复杂度上均优于已知最佳结果，第二种算法在近似比方面也更具优势。