title: Clustering of solutions in the random satisfiability problem.
abstract: Using elementary rigorous methods we prove the existence of a clustered phase in the random K-SAT problem, for K > or = 8. In this phase the solutions are grouped into clusters which are far away from each other. The results are in agreement with previous predictions of the cavity method and give a rigorous confirmation to one of its main building blocks. It can be generalized to other systems of both physical and computational interest.
authors.affiliation: Laboratoire de Physique Théorique et Modèles Statistiques, bâtiment 100, Université Paris-Sud, Orsay, France.
authors.forename: M
authors.initials: M
authors.lastname: Mézard
authors.forename: T
authors.initials: T
authors.lastname: Mora
authors.forename: R
authors.initials: R
authors.lastname: Zecchina