  We construct a matrix model that reproduces the topological string partition
function on arbitrary toric Calabi-Yau 3-folds. This demonstrates, in accord
with the BKMP "remodeling the B-model" conjecture, that Gromov-Witten
invariants of any toric Calabi-Yau 3-fold can be computed in terms of the
spectral invariants of a spectral curve. Moreover, it proves that the
generating function of Gromov-Witten invariants is a tau function for an
integrable hierarchy. In a follow-up paper, we will explicitly construct the
spectral curve of our matrix model and argue that it equals the mirror curve of
the toric Calabi-Yau manifold.
