Phase Transitions Workshop Program

Dimitris Achlioptas (UC Santa Cruz) On the solution space geometry of random CSPs For a number of random constraint satisfaction problems, such as random k-SAT and random graph coloring, we now have excellent estimates of the largest constraints-to-variables ratio for which they have solutions. These estimates imply that all known polynomialtime algorithms stop finding solutions much before solutions cease to exist. To understand the origin of this phenomenon we study the evolution of the structure of the space of solutions in random CSPs as constraints are added. In particular, we will survey both what physicists hypothesize happens in this evolution, and what has been rigorously proven so far. We will see that the rigorous results are both in agreement with the physics predictions and help demystify Survey Propagation, an extremely successful heuristic proposed by physicists for random