Minimum weight Euclidean t-spanner is NP-hard ?
Given a set P of points in the plane, an Euclidean t-spanner for P is a geometric graph that preserves the Euclidean distances between every pair of points in P up to a constant factor t. The weight of a geometric graph refers to the total length of its edges. In this paper we show that the problem of deciding whether there exists an Euclidean t-spanner, for a given set of points in the plane, of weight at most w  is NP-hard for every real constant t>1 t > 1 , both whether planarity of the t-spanner is required or not.
np-hardness computational geometry geometry spanner