  Amplitudes in open topological string theory may be described completely by
certain A-infinity-categories. We detail a general construction of all cyclic
minimal models for a given A-infinity-algebra and apply this result to the case
of N=2 supersymmetric Landau-Ginzburg models. This allows to solve the
tree-level theory in the sense that all amplitudes and hence the effective
superpotential can be computed algorithmically. Furthermore, the construction
provides a novel derivation of the topological metric of such models.
