English

Computing a Minimum-Dilation Spanning Tree is NP-hard

Computational Geometry 2007-05-23 v1

Abstract

In a geometric network G = (S, E), the graph distance between two vertices u, v in S is the length of the shortest path in G connecting u to v. The dilation of G is the maximum factor by which the graph distance of a pair of vertices differs from their Euclidean distance. We show that given a set S of n points with integer coordinates in the plane and a rational dilation delta > 1, it is NP-hard to determine whether a spanning tree of S with dilation at most delta exists.

Keywords

Cite

@article{arxiv.cs/0703023,
  title  = {Computing a Minimum-Dilation Spanning Tree is NP-hard},
  author = {Otfried Cheong and Herman Haverkort and Mira Lee},
  journal= {arXiv preprint arXiv:cs/0703023},
  year   = {2007}
}