Computing a Minimum-Dilation Spanning Tree is NP-hard
<|reference_start|>Computing a Minimum-Dilation Spanning Tree is NP-hard: 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.<|reference_end|>
@article{cheong2007computing,
    title={Computing a Minimum-Dilation Spanning Tree is NP-hard},
    author={Otfried Cheong, Herman Haverkort, Mira Lee},
    journal={arXiv preprint arXiv:cs/0703023},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0703023},
    primaryClass={cs.CG}
}