Minimum weight Euclidean t-spanner is NP-hard

Paz Carmi, Lilach Chaitman-Yerushalmi

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish
Pages (from-to)30-42
Number of pages13
JournalJournal of Discrete Algorithms
StatePublished - 1 Sep 2013


  • Computational geometry-Geometry spanner
  • NP-hardness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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