  We study the dynamical exponent $z$ for the directed percolation depinning
(DPD) class of models for surface roughening in the presence of quenched
disorder. We argue that $z$ for $(d+1)$ dimensions is equal to the exponent
$d_{\rm min}$ characterizing the shortest path between two sites in an
isotropic percolation cluster in $d$ dimensions. To test the argument, we
perform simulations and calculate $z$ for DPD, and $d_{\rm min}$ for
percolation, from $d = 1$ to $d = 6$.
