Conditions for unique graph realizations
SIAM Journal on Computing
Theory of semidefinite programming for sensor network localization
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Connected rigidity matroids and unique realizations of graphs
Journal of Combinatorial Theory Series B
A Theory of Network Localization
IEEE Transactions on Mobile Computing
On the Infinitesimal Rigidity of Bar-and-Slider Frameworks
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Universal rigidity: towards accurate and efficient localization of wireless networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
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In the network localization problem the locations of some nodes (called anchors) as well as the distances between some pairs of nodes are known, and the goal is to determine the location of all nodes. The localization problem is said to be solvable (or uniquely localizable) if there is a unique set of locations consistent with the given data. Recent results from graph rigidity theory made it possible to characterize the solvability of the localization problem in two dimensions. In this paper we address the following related optimization problem: given the set of known distances in the network, make the localization problem solvable by designating a smallest set of anchor nodes. We develop a polynomial-time 3-approximation algorithm for this problem by proving new structural results in graph rigidity and by using tools from matroid theory.