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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 NPcomplete 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( √ 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.

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