Hardness results for computing optimal locally Gabriel graphs

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
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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