In this study, we identify a class of redundant transitivity constraints in a 0-1 integer linear programming formulation of the clique partitioning problem. The transitivity constraints in this class can be removed from the formulation without changing the optimal solution set, although each transitivity constraint defines a facet of the associated polytope. This leads to a smaller formulation that is particularly effective for instances arising from correlation clustering, where edge weights are drawn from $\{-1,1\}$. Our computational experiments show that the resulting formulation outperforms existing formulations on such instances.

翻译：本研究中，我们在团划分问题的0-1整数线性规划模型中识别出一类冗余传递性约束。尽管每个传递性约束均定义了关联多面体的一个面，但该类约束可从模型中移除而不改变最优解集。这导致一种规模更小的模型，特别适用于边权取自$\{-1,1\}$的相关聚类实例。计算实验表明，针对此类实例，所得模型优于现有模型。