Minimum Weight Euclidean t-spanner is NP-Hard
Computational Geometry
2012-09-05 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1209.0679,
title = {Minimum Weight Euclidean t-spanner is NP-Hard},
author = {Paz Carmi and Lilach Chaitman-Yerushalmi},
journal= {arXiv preprint arXiv:1209.0679},
year = {2012}
}