Metric Dimension for Gabriel Unit Disk Graphs is NP-Complete
Computational Complexity
2013-06-11 v1 Data Structures and Algorithms
Abstract
We show that finding a minimal number of landmark nodes for a unique virtual addressing by hop-distances in wireless ad-hoc sensor networks is NP-complete even if the networks are unit disk graphs that contain only Gabriel edges. This problem is equivalent to Metric Dimension for Gabriel unit disk graphs. The Gabriel edges of a unit disc graph induce a planar O(\sqrt{n}) distance and an optimal energy spanner. This is one of the most interesting restrictions of Metric Dimension in the context of wireless multi-hop networks.
Cite
@article{arxiv.1306.2187,
title = {Metric Dimension for Gabriel Unit Disk Graphs is NP-Complete},
author = {Stefan Hoffmann and Egon Wanke},
journal= {arXiv preprint arXiv:1306.2187},
year = {2013}
}
Comments
A brief announcement of this result has been published in the proceedings of ALGOSENSORS 2012