Conditions for unique graph realizations
SIAM Journal on Computing
Ad-hoc networks beyond unit disk graphs
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Localization and routing in sensor networks by local angle information
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing
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Many applications in sensor networks require positional information of the sensors. Recovering node positions is closely related to graph realization problems for geometric graphs. Here, we address the case where nodes have angular information. Whereas Bruck et al. proved that the corresponding realization problem together with unit-disk-graph-constraints is $\mathcal{NP}$-hard [2], we focus on rigid components which allow both efficient identification and fast, unique realizations. Our technique allows to identify maximum rigid components in graphs with partially known rigid components using a reduction to maximum flow problems. This approach is analyzed for the two-dimensional case, but can easily be extended to higher dimensions.