What is known
The Douglas-Peucker algorithm serves to reduce the number of vertices of a polygonal chain while simultaneously preserving its original shape. The original polygonal chain in (a) is reduced to the green shape in (d).
What I want
So far each vertex was connected to maximum $2$ other vertices (as the curve in the previous example is closed there are no singly-connected vertices). Now I want to perform coarsening on branched lines, i.e. the number of connecting vertices can be larger than $2$ as shown in the next simple example (black: original, green: simplified). Is there already a modified Douglas-Peucker algorithm for this case?
How I could solve it
I could list all partitions in paths and then select the simplification with lowest number of vertices. To test all partitions would be not very efficient as the number of partitions quickly increases with the number of vertices. For the example we just have $3$ partitions that each consist of $2$ polylines (red, blue) that all have to be tested. More about this kind of partition can be found here.
