The authors want to find an inpolygon of shortest circumference in a given convex polygon with m vertices. Focke evolutes the polygon under successive reflection, lays a line corresponding to an inpolygon through all concave vertices of this ‘channel’ and shortens the line by a descent method with complexity O(m3) to an optimum. The authors determine a first active vertex of the channel with complexity O(m), lay a straight line through this vertex and lengthen the line by a trivial method with complexity O(m2) to a feasible line (optimum).
