A Combinatorial Approximation Algorithm for Correlation Clustering

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).