Is there any known algorithm for computing the Heegard-Floer homology of a given 3-manifold from a Heegard diagram?

I am trying to compute it from the definition, and most of the steps can be put in an algorithmic way (in the sense that they can be programmed into a computer, for example), but at some point you need to count points in a moduli space of a homotopy class (which is not even uniquely determined). I really see no way to automatically compute this.

Is there any purelly combinatorial way to compute these groups?