Random Constraint Satisfaction Problems

Random instances of constraint satisfaction problems such as &-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r = m/n where solutions are known to exist with probability close to one due to non-constructive arguments. However, no algorithms are known to find solutions efficiently with a non-vanishing probability at even much lower densities. This fact appears to be related to a phase transition in the set of all solutions. The goal of this extended abstract is to provide a perspective on this phenomenon, and on the computational challenge that it poses.