On the redundancy of transitivity constraints in the clique partitioning problem

TL;DR

This paper identifies redundant transitivity constraints in a 0-1 ILP formulation of the clique partitioning problem, leading to a smaller, more efficient formulation for correlation clustering instances.

Contribution

It demonstrates that certain transitivity constraints can be removed without affecting optimal solutions, improving computational performance.

Findings

Removing these constraints results in a smaller, more efficient formulation.

The new formulation outperforms existing ones on correlation clustering instances.

Computational experiments validate the effectiveness of the reduced formulation.

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.