Clustering of solutions in the random satisfiability problem

M. Mezard 1, T. Mora 1, R. Zecchina 2

Physical Review Letters 94 (2005) 197205

Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\\geq 8$. 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.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2. The Abdus Salam International Centre for Theoretical Physics,
    ICTP Trieste