Minimum Weight Euclidean t-spanner is NP-Hard

Paz Carmi; Lilach Chaitman-Yerushalmi

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arXiv · 1209.0679

Minimum Weight Euclidean t-spanner is NP-Hard

Paz Carmi·Lilach Chaitman-Yerushalmi

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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.

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Paz Carmi, Lilach Chaitman-Yerushalmi. 2012-09-04. Minimum Weight Euclidean t-spanner is NP-Hard. https://arxiv.org/abs/1209.0679

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