Exploiting sparsity for the min k-partition problem

TL;DR

This paper introduces new compact integer linear and semidefinite formulations for the min k-partition problem that leverage graph sparsity and chordal decomposition to improve computational efficiency.

Contribution

The authors develop novel formulations exploiting sparsity and chordal decomposition, significantly enhancing solution methods for the min k-partition problem.

Findings

New formulations outperform existing methods in computational tests.

Exploiting sparsity reduces problem complexity.

Chordal decomposition enables scalable solutions.

Abstract

The minimum k-partition problem is a challenging combinatorial problem with a diverse set of applications ranging from telecommunications to sports scheduling. It generalizes the max-cut problem and has been extensively studied since the late sixties. Strong integer formulations proposed in the literature suffer from a prohibitive number of valid inequalities and integer variables. In this work, we introduce two compact integer linear and semidefinite reformulations that exploit the sparsity of the underlying graph and develop fundamental results leveraging the power of chordal decomposition. Numerical experiments show that the new formulations improve upon state-of-the-art.