Computing Geometric Minimum-Dilation Graphs Is NP-Hard

We prove that computing a geometric minimum-dilation graph on a given set of points in the plane, using not more than a given number of edges, is an NP-hard problem, no matter if edge crossings are allowed or forbidden. We also show that the problem remains NP-hard even when a minimum-dilation tour or path is sought; not even an FPTAS exists in this case.

• Type: Conference
• Year: 2006
• Where: GD
• Authors: Rolf Klein, Martin Kutz
• Keywords: Computer Graphics, Edge Crossings, GD 2006, Geometric Minimum-dilation Graph, NP-hard Problem