On the redundancy of transitivity constraints in the clique partitioning problem

2026-05-02

AI Summary

This study addresses the challenge of excessive model size and low solution efficiency in the clique partitioning problem caused by redundant transitivity constraints. The authors identify a class of globally redundant transitivity constraints within 0–1 integer linear programming formulations: although each individual constraint defines a facet of the feasible polyhedron, their collective removal—under correlation clustering instances with edge weights restricted to {−1, 1}—does not alter the set of optimal solutions. Drawing on polyhedral theory and computational experiments, the proposed simplified model substantially reduces problem scale and demonstrates markedly improved computational efficiency compared to existing modeling approaches for correlation clustering tasks.

Abstract

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.

Problem

• clique partitioning
• transitivity constraints
• redundancy
• integer linear programming
• correlation clustering

Innovation

• clique partitioning
• transitivity constraints
• redundancy
• integer linear programming
• correlation clustering