Clever algorithms for glasses work by time reparameterization

The ultraslow dynamics of glass-formers has been explained by two views often considered as mutually exclusive: One invokes locally hindered mobility, and the other rests on the complexity of the configuration space. Here, we show that time evolution responds strongly to details of the dynamics by changing the speed of time flow: It has time-reparameterization softness. This finding reconciles both views: While local constraints reparameterize the flow of time, the global landscape determines relationships between different correlations at the same times. We show that modern algorithms developed to accelerate the relaxation to equilibrium act by changing the time reparameterization. Their success thus relies on their ability to exploit reparameterization softness. We conjecture that these results extend beyond the realm of glasses to the optimization of more general constraint satisfaction problems and to broader classes of algorithms.