2012/09/04 by Carmi, Paz, Chaitman-Yerushalmi, Lilach · 2 citations
#Computational Geometry (cs.CG) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1209.0679
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, both whether planarity of the t-spanner is required or not.