Computing a Minimum-Dilation Spanning Tree is NP-hard

Details Computing a Minimum-Dilation Spanning Tree is NP-hard Computing a Minimum-Dilation Spanning Tree is NP-hard

2007-03-06

arxiv.org/abs/cs/0703023v1

Computer Science

Computational Geometry

Scientific paper

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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