Towards the computation of the convex hull of a configuration from its corresponding separating matrix

In this paper, we cope with the following problem: compute the size of the convex hull of a configuration C, where the given data is the number of separating lines between any two points of the configuration (where the lines are generated by pairs of other points of the configuration). We give an algorithm for the case that the convex hull is of size 3, and a partial algorithm and some directions for the case that the convex hull is of size bigger than 3.