Constraint optimisation and landscapes

We describe an effective landscape introduced in [1] for the analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring. This geometric construction reexpresses such problems in the more familiar terms of optimisation in rugged energy landscapes. In particular, it allows one to understand the puzzling fact that unsophisticated programs are successful well beyond what was considered to be the `hard’ transition, and suggests an algorithm defining a new, higher, easy-hard frontier.