Matrix factorisations and open topological string theory

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.