We introduce a lower bounding technique for the min max correlation clustering problem and, based on this technique, a combinatorial 4-approximation algorithm for complete graphs. This improves upon the previous best known approximation guarantees of 5, using a linear program formulation (Kalhan et al., 2019), and 40, for a combinatorial algorithm (Davies et al., 2023). We extend this algorithm by a greedy joining heuristic and show empirically that it improves the state of the art in solution quality and runtime on several benchmark datasets.

翻译：我们针对极小最大相关性聚类问题提出了一种下界构造技术，并基于该技术给出了完全图上的组合4-近似算法。该结果优于先前已知的最优近似保证：基于线性规划方法的5-近似（Kalhan等，2019）和组合算法的40-近似（Davies等，2023）。我们通过贪心合并启发式方法对该算法进行了扩展，实验结果表明，在多个基准数据集上，该算法在解的质量和运行时间方面均提升了现有技术水平。