Computing a minimum-dilation spanning tree is NP-hard

Authors:
Otfried Cheong;Herman Haverkort;Mira Lee
Affiliations:
Department of Computer Science, Korea Advanced Institute of Science & Technology, Daejeon, South Korea;Department of Mathematics and Computing Science, TU Eindhoven, Eindhoven, The Netherlands;Department of Computer Science, Korea Advanced Institute of Science & Technology, Daejeon, South Korea
Venue:
Computational Geometry: Theory and Applications
Year:
2008

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Abstract

In a geometric network G=(S,E), the graph distance between two vertices u,v@?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 @d1, it is NP-hard to determine whether a spanning tree of S with dilation at most @d exists.