Detecting instability in concavity trees

A simple algorithm is described for detecting the possibility of encountering instability in the set of concavity trees generated from a class of very similar shapes (i.e. those which can be represented by a single archetype). The algorithm can detect instability in deep m-concavities but is unable to accommodate shallow depressions in the edge. However, an earlier paper showed that the latter can be tolerated by a simple modification to the concavity-tree generator. Once the potential for instability has been detected, it is usually obvious what course of action is necessary; the instability detector is intended to avoid applying tree-matching procedures in an inappropriate way.