Clustering of solutions in the random satisfiability problem

Details Clustering of solutions in the random satisfiability problem Clustering of solutions in the random satisfiability problem

2005-04-04

arxiv.org/abs/cond-mat/0504070v1

Phys. Rev. Lett. 94, 197205 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.94.197205

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.

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