English

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}
}
R2 v1 2026-06-21T21:59:36.154Z