  High energy hard scattering in large $N_{c}$ limit can be described by the
QCD dipole model. In this paper, single, double and triple BFKL pomeron
exchange amplitudes are computed explicitly within the dipole model. Based on
the calculation, the general formula
$\gamma^{(k)*}_{0}=\chi^{-1}(k\chi({1/2}))$ which governs the anomalous
dimension of $1\Rightarrow k$ amplitude is conjectured. As far as the unitarity
problem is concerned, we find that the anomalous dimension $\gamma$ varies from
graph to graph due to the DGLAP evolution. In the end, a comparison between
this computation and reggeon field theory is provided.
