Optimally sparse spanners in 3-dimensional Euclidean space
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
SIAM Journal on Discrete Mathematics
A new way to weigh Malnourished Euclidean graphs
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Geometric Spanner Networks
Computing a minimum-dilation spanning tree is NP-hard
Computational Geometry: Theory and Applications
Computing the Greedy Spanner in Near-Quadratic Time
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Computing geometric minimum-dilation graphs is NP-hard
GD'06 Proceedings of the 14th international conference on Graph drawing
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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 t1, both whether planarity of the t-spanner is required or not.