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Computing a Minimum-Dilation Spanning Tree is NP-hard

Otfried Cheong·Herman Haverkort·Mira Lee
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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.

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Otfried Cheong, Herman Haverkort, Mira Lee. 2007-03-06. Computing a Minimum-Dilation Spanning Tree is NP-hard. https://arxiv.org/abs/cs/0703023

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