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The sensor network localization problem with distance information is to determine the positions of all the sensors in a network given the positions of some sensors and the distances between some pairs of sensors. One approach to localize a large network is to divide the network into smaller subnetworks whereby each subnetwork is localized in its own coordinate system. We present two algorithms which use linear algebra methods for computing the actual sensor positions given the local solutions of a collection of subnetworks. We also use graph rigidity theory to characterize collections of subnetworks for which the algorithms are applicable.