  We consider discrete models of kinetic rough interfaces that exhibit
space-time scale-invariance in height-height correlation. A generic scaling
theory implies that the dynamical structure factor of the height profile can
uniquely characterize the underlying dynamics. We provide a finite-time scaling
that systematically allows an estimation of the critical exponents and the
scaling functions, eventually establishing the universality class accurately.
As an illustration, we investigate a class of self-organized interface models
in random media with extremal dynamics. The isotropic version shows a faceted
pattern and belongs to the same universality class (as shown numerically) as
the Sneppen (model A). We also introduce an anisotropic version of the Sneppen
(model A) and suggest that the model belongs to the universality class of the
tensionless one-dimensional Kardar-Parisi-Zhang equation.
