In this study Dijkgraaf and Vafa showed that the closed string partition function of the topological B-model on a Calabi-Yau of the form $uv-H(x,y)=0$ coincides with the free energy of a certain matrix model.
Then, after taking the double-scaling limit, they get an identification between the B-model partition function and the minimal string partition function. The latter is a minimal model coupled to the Liouville theory, and the equation $H(x,y)=0$ corresponds to what is known as the minimal string Riemann surface (see http://arxiv.org/abs/hep-th/0312170). For the $(p,q)$ minimal model (without any insertions) one gets $H(x,y)=y^p+x^q$.
There are two kinds of branes in the Liouville theory: FZZT and ZZ, where the FZZT branes are parametrized (semiclassically) by the points on the Riemann surface $H(x,y)=0$.
What are the equivalents of the FZZT and ZZ open string partition functions in the B-model?