Maximum Rigid Components as Means for Direction-Based Localization in Sensor Networks

Many applications or algorithms in sensor networks require positional information of the sensors. Most approaches for this problem rely either on distances between communicating node pairs or on local angular information. Although distance-based methods are widespread, we here present a technique for direction-based localization in general networks. Whereas Bruck et al. proved that the corresponding realization problem can be solved by Linear Programming but becomes NP-hard [2] for unit-disk-graphs, we focus on rigid components which allow both efficient identification and fast, unique realizations. We propose a technique to group small rigid components that can be found by standard techniques to maximum such components using a reduction to maximum flow problems. The method is analyzed for the two-dimensional case, but can easily be extended to higher dimensions. By evaluating our approach on (quasi-)unit-disk graphs, we observe that the required density in order to localize a large percentage of the network is comparably small to previous methods.