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We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase diagram in temperature, the connections with the glass transition phenomenology in physics, and the related algorithmic issues.
We show that for any odd $k$ and any instance of the Max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a $frac{1}{2} + Omega(1/sqrt{D})$ fraction of constraints, where $D$ is a boun
Random constraint satisfaction problems undergo several phase transitions as the ratio between the number of constraints and the number of variables is varied. When this ratio exceeds the satisfiability threshold no more solutions exist; the satisfia
We study the phase diagram and the algorithmic hardness of the random `locked constraint satisfaction problems, and compare them to the commonly studied non-locked problems like satisfiability of boolean formulas or graph coloring. The special proper
The typical complexity of Constraint Satisfaction Problems (CSPs) can be investigated by means of random ensembles of instances. The latter exhibit many threshold phenomena besides their satisfiability phase transition, in particular a clustering or
We introduce and study the random locked constraint satisfaction problems. When increasing the density of constraints, they display a broad clustered phase in which the space of solutions is divided into many isolated points. While the phase diagram