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., 2023a). 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：我们针对最小最大值相关聚类问题引入了一种下界技术，并基于该技术提出了一个针对完全图的组合4-近似算法。这改进了此前已知的最佳近似保证，即基于线性规划公式的5-近似（Kalhan等，2019）和采用组合算法的40-近似（Davies等，2023a）。我们通过一种贪心合并启发式方法对该算法进行了扩展，并在多个基准数据集上实验表明，其在解质量和运行时方面优于现有技术。