Khopkar, Abhijeet and Govindarajan, Sathish (2012) Hardness results for computing optimal locally Gabriel graphs. In: 24th Canadian Conference on Computational Geometry, August 8-10, 2012, Charlottetown, Prince Edward Island, Canada.
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Abstract
Delaunay and Gabriel graphs are widely studied geo-metric proximity structures. Motivated by applications in wireless routing, relaxed versions of these graphs known as Locally Delaunay Graphs (LDGs) and Lo-cally Gabriel Graphs (LGGs) have been proposed. We propose another generalization of LGGs called Gener-alized Locally Gabriel Graphs (GLGGs) in the context when certain edges are forbidden in the graph. Unlike a Gabriel Graph, there is no unique LGG or GLGG for a given point set because no edge is necessarily in-cluded or excluded. This property allows us to choose an LGG/GLGG that optimizes a parameter of interest in the graph. We show that computing an edge max-imum GLGG for a given problem instance is NP-hard and also APX-hard. We also show that computing an LGG on a given point set with dilation ≤k is NP-hard. Finally, we give an algorithm to verify whether a given geometric graph G= (V, E) is a valid LGG.
Item Type: | Conference Paper |
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Publisher: | Pacific Institute for the Mathematical Sciences |
Additional Information: | Copyright of this article belongs to Pacific Institute for the Mathematical Sciences. |
Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |
Date Deposited: | 08 Nov 2013 05:17 |
Last Modified: | 08 Nov 2013 05:17 |
URI: | http://eprints.iisc.ac.in/id/eprint/47725 |
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