Surface Diffusion in the Solid-on-Solid Model

We present results in $1+1$ and $2+1$ dimensions for surface diffusion controlled profile relaxation for the solid-on-solid model above and below the roughening transition. For all cases examined we found that the characteristic time scale $\tau$ for the decay of a sinusoidal profile scaled with the wavelength $L$ as $\tau \sim L^z$ where $z\cong 4$. These results can be understood in terms of the anomalous diffusion displayed by tracer atoms whose root mean square displacement scaled as $t^{1/4}$.