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Computing Geometric Minimum-Dilation Graphs is NP-Hard

Klein, Rolf and Kutz, Martin (2007) Computing Geometric Minimum-Dilation Graphs is NP-Hard. [Conference Paper]

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Abstract

Consider a geometric graph G, drawn with straight lines in the plane. For every pair a,b of vertices of G, we compare the shortest-path distance between a and b in G (with Euclidean edge lengths) to their actual Euclidean distance in the plane. The worst-case ratio of these two values, for all pairs of vertices, is called the vertex-to-vertex dilation of G. We prove that computing a minimum-dilation graph that connects a given n-point set in the plane, using not more than a given number m of edges, is an NP-hard problem, no matter if edge crossings are allowed or forbidden. In addition, we show that the minimum dilation tree over a given point set may in fact contain edge crossings.

Item Type:Conference Paper
Classifications:Z Theory > Z.001 General
ID Code:774
Deposited By:GDEA, Administration
Deposited On:04 May 2007
Last Modified:18 Sep 2008 13:09
Alternative Locations:http://www.springer.com/dal/home/computer/lncs?SGWID=1-164-22-173721109-0

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