We study the problem of augmenting the locus N of a plane Euclidean network N
by inserting iteratively a finite set of segments, called shortcut set, while reducing
the diameter of the locus of the resulting network. We first characterize the existence
of shortcut sets, and compute shortcut sets in polynomial time providing an upper
bound on their size. Then, we analyze the role of the convex hull of N when
inserting a shortcut set. As a main result, we prove that one can always determine in
polynomial time whether inserting only one segment suffices to reduce the diameter.Ministerio de Economía y Competitividad MTM2014-60127-PJunta de Andalucía FQM-016
