Conditions for unique graph realizations
SIAM Journal on Computing
Dynamic fine-grained localization in Ad-Hoc networks of sensors
Proceedings of the 7th annual international conference on Mobile computing and networking
Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework
SIAM Journal on Optimization
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
Semidefinite programming for ad hoc wireless sensor network localization
Proceedings of the 3rd international symposium on Information processing in sensor networks
Extremal Graph Theory
Discrete & Computational Geometry
Connected rigidity matroids and unique realizations of graphs
Journal of Combinatorial Theory Series B
A semidefinite programming approach to tensegrity theory and realizability of graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Semidefinite programming based algorithms for sensor network localization
ACM Transactions on Sensor Networks (TOSN)
A Theory of Network Localization
IEEE Transactions on Mobile Computing
Low-Dimensional Embedding with Extra Information
Discrete & Computational Geometry
Theory of semidefinite programming for Sensor Network Localization
Mathematical Programming: Series A and B
Second-Order Cone Programming Relaxation of Sensor Network Localization
SIAM Journal on Optimization
Further Relaxations of the Semidefinite Programming Approach to Sensor Network Localization
SIAM Journal on Optimization
Localization and routing in sensor networks by local angle information
ACM Transactions on Sensor Networks (TOSN)
Wireless Ad Hoc and Sensor Networks: Theory and Applications
Wireless Ad Hoc and Sensor Networks: Theory and Applications
Distributed localization for anisotropic sensor networks
ACM Transactions on Sensor Networks (TOSN)
Exploiting Sparsity in SDP Relaxation for Sensor Network Localization
SIAM Journal on Optimization
Uniquely localizable networks with few anchors
ALGOSENSORS'06 Proceedings of the Second international conference on Algorithmic Aspects of Wireless Sensor Networks
Sensor network localization using sensor perturbation
ACM Transactions on Sensor Networks (TOSN)
Universal Rigidity and Edge Sparsification for Sensor Network Localization
SIAM Journal on Optimization
Sensor network localization by eigenvector synchronization over the euclidean group
ACM Transactions on Sensor Networks (TOSN)
Toward collinearity-aware and conflict-friendly localization for wireless sensor networks
Computer Communications
OFA: An optimistic approach to conquer flip ambiguity in network localization
Computer Networks: The International Journal of Computer and Telecommunications Networking
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A fundamental problem in wireless ad-hoc and sensor networks is that of determining the positions of nodes. Often, such a problem is complicated by the presence of nodes whose positions cannot be uniquely determined. Most existing work uses the notion of global rigidity from rigidity theory to address the non-uniqueness issue. However, such a notion is not entirely satisfactory, as it has been shown that even if a network localization instance is known to be globally rigid, the problem of determining the node positions is still intractable in general. In this paper, we propose to use the notion of universal rigidity to bridge such disconnect. Although the notion of universal rigidity is more restrictive than that of global rigidity, it captures a large class of networks and is much more relevant to the efficient solvability of the network localization problem. Specifically, we show that both the problem of deciding whether a given network localization instance is universally rigid and the problem of determining the node positions of a universally rigid instance can be solved efficiently using semidefinite programming (SDP). Then, we give various constructions of universally rigid instances. In particular, we show that trilateration graphs are generically universally rigid, thus demonstrating not only the richness of the class of universally rigid instances, but also the fact that trilateration graphs possess much stronger geometric properties than previously known. Finally, we apply our results to design a novel edge sparsification heuristic that can reduce the size of the input network while provably preserving its original localization properties. One of the applications of such heuristic is to speed up existing convex optimization-based localization algorithms. Simulation results show that our speedup approach compares very favorably with existing ones, both in terms of accuracy and computation time.