  Given a set of sources and a set of sinks as points in the Euclidean plane, a
directed network is a directed graph drawn in the plane with a directed path
from each source to each sink. Such a network may contain nodes other than the
given sources and sinks, called Steiner points. We characterize the local
structure of the Steiner points in all shortest-length directed networks in the
Euclidean plane. This characterization implies that these networks are
constructible by straightedge and compass. Our results build on unpublished
work of Alfaro, Campbell, Sher, and Soto from 1989 and 1990. Part of the proof
is based on a new method that uses other norms in the plane. This approach
gives more conceptual proofs of some of their results, and as a consequence, we
also obtain results on shortest directed networks for these norms.
