Existence of shortest directed networks in \(\mathbb{R}^ 2\)
This paper establishes the existence of a shortest directed network in \(\mathbb{R}^ 2\) connecting all of a given set of starting points to all of a given set of ending points. In such networks, up to six segments sometimes meet at a point. The main difficulty is bounding the number of nodes, since shortest directed networks may contain cycles. It is an open question whether existence holds in \(\mathbb{R}^ n\).
scientific article; zbMATH DE number 769657