Clustering of solutions in the random satisfiability problem

Mezard, M.; Mora, T.; Zecchina, R.

Clustering of solutions in the random satisfiability problem

Authors

Mezard, M.

Mora, T.

Zecchina, R.

Description

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.
4 pages, 1 figure