# How to create a branch network from several input points to an unique outlet in minimizing the distances?

I am searching a way to "hydrologically" connect upstream points to a unique downstream outlet by creating an optimized stream network as pictured below...

The cummulated lenght of the stream lines should be minimized.

Otherwise the stream network should remains confined within a defined polygon...

I only know the input points (red) and the output (green) and the polygon. There is no other constraints

Does anyone know how to do it ?...

I searched on the web all the morning but without succeed

No I rightly try to do it without considering the topography... Just a flat (or approx flat) surface. That's why I am searching a way for so long time :-)

It is an hyopthetical area.

Imagine that you are in you bath.. the water level rises up and overflow on a downstream threshold - at a corner of you bath..

Then you add a few particles at different corners of your bath (upstream) and you try now to sketch what will be their circulation to reach the threshold by forming an optimized network.. The stream network (as I draw on the right) should be minimum regarding the particles input.

Am I understood ? :-)

• If this is a stream network, then you wouldn't necessarily want the shortest path, but would want to have the correct path based on the topography of the area. Is this an actual area, or a hypothetical? Do you have any kind of topographic information for this area? Conversely, if this is hypothetical, then the picture on the right is almost correct, except make those straight lines with the intersections being where one is perpendicular to the other as that will be the closest, and thus shortest total path. More detail would help clarify your intended result. Dec 6, 2012 at 4:04
• As stated, this is a (constrained) Steiner Tree problem. Feb 4, 2013 at 14:50