Using elementary rigorous methods we prove the existence of a clustered phase in the
random K-SAT problem, for K≥ 8. In this phase the solutions are grouped into clusters …

An analysis of the average properties of a local search procedure (RandomWalkSAT) for the
satisfaction of random Boolean constraints is presented. Depending on the ratio α of …

We study the problem of satisfiability of randomly chosen clauses, each with K Boolean
variables. Using the cavity method at zero temperature, we find the phase diagram for the K …

Using the cavity equations of Mézard, Parisi, and Zecchina Science 297 (2002), 812;
Mézard and Zecchina, Phys Rev E 66 (2002), 056126 we derive the various threshold …

We study the set of solutions of random k-satisfiability formulas through the cavity method. It
is known that, for an interval of the clause-to-variables ratio, this decomposes into an …

We study a simple and exactly solvable model for the generation of random satisfiability
problems. These consist of γ N random boolean constraints which are to be satisfied …

A variational approach to finite connectivity spin-glass-like models is developed and applied
to describe the structure of optimal solutions in random satisfiability problems. Our …

Random k-SAT is the single most intensely studied example of a random constraint
satisfaction problem. But despite substantial progress over the past decade, the threshold for …

A local search algorithm solving an NP-complete optimization problem can be viewed as a
stochastic process moving in an'energy landscape'towards eventually finding an optimal …

Random constraint satisfaction problems (CSP) have been studied extensively using
statistical physics techniques. They provide a benchmark to study average case scenarios …