Separable clusterings of a data set can be represented as the vertices of the so-called partition polytopes. In many applications, a transition between two given clusterings is required. Each step of this transition is supposed to keep separation of the current clusters.

Such a transition can be modeled as an edge walk in the partition polytopes. An implementation of such a scheme is a significant challenge, in particular due to the lack of an explicit representation of these polytopes. We discuss the basics of the underlying mathematics and then turn to details of a successful implementation.