Spectral bounds for the maximum cut problem

Walid Ben-Ameur (1, 2, 3, 4) , José Neto (2, 3, 4)

1 METHODES-SAMOVAR - Méthodes et modèles pour les réseaux
2 TSP - RS2M - Département Réseaux et Services Multimédia Mobiles
3 SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
4 CNRS - Centre National de la Recherche Scientifique

The maximum cut problem is a classical combinatorial optimization problem that is known to be NP-hard in general. In the present article, we provide some new lower and upper bounds that are based on the eigenvalues of the weight matrix with modified diagonal entries. Namely, we show that some upper bounds presented here are generally better than the SDP bound introduced by Goemans and Williamson, JACM 42 (1995), 1115-1145. We also discuss the complexity of computing these bounds and provide some preliminary computational results

Mots clés: Combinatorial optimization; Maximum cut; Eigenvalues; Relaxations

Domaines: Algorithme et structure de données [cs.DS]

Walid Ben-Ameur, José Neto. Spectral bounds for the maximum cut problem. Networks, 2008, 52 (1), pp.8 - 13. ⟨10.1002/net.20220⟩. ⟨hal-01326524⟩