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 4, 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：针对最小最大相关聚类问题，我们引入一种下界技术，并基于该技术提出一个面向完全图的组合4-近似算法。这改进了此前已知的最佳近似保证：基于线性规划公式的5-近似算法（Kalhan等，2019）以及组合算法的4-近似算法（Davies等，2023）。我们通过贪心连接启发式方法对该算法进行扩展，并在多个基准数据集上通过实验证明，该算法在解的质量和运行时间上均提升了当前最优水平。