Using Local Graph Topology to Model Hard Binary Constraint Satisfaction Problems

, have recently shown how to model hard binary Constraint Satisfaction Problems (CSPs). Their model parameterizes CSPs with a global constraint tightness. This paper presents a new model which parameterizes CSPs with local constraint tightness parameters. The new model combines Smith's predictor of the transition point ^ p 2crit with local graph topology. We show empirically that the new model produces problems that are on average as hard or harder to search than the old model, produces problems with a wide range of local constraint tightness, and produces problems that are closer to the peak of the phase transition. We show for sparse constraint graphs that the new model produces problems much closer to the phase transition than the old model. Our results indicate that the underlying structure of a problem needs to be included in models of hard problems.