Shortcut sets for plane Euclidean networks (Extended abstract)

We study the problem of augmenting the locus Nℓ 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 Nℓ 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.