SIAM Journal on Discrete Mathematics
The molecule problem: determining conformation from pairwise distances
The molecule problem: determining conformation from pairwise distances
Conditions for unique graph realizations
SIAM Journal on Computing
A proof of Connelly's conjecture on 3-connected circuits of the rigidity matroid
Journal of Combinatorial Theory Series B
Conditions Unique Graph Embeddings
Conditions Unique Graph Embeddings
Discrete & Computational Geometry
The d-dimensional rigidity matroid of sparse graphs
Journal of Combinatorial Theory Series B
On the existence of k edge-disjoint 2-connected spanning subgraphs
Journal of Combinatorial Theory Series B
A note on the trackability of dynamic sensor networks
Proceedings of the first ACM international workshop on Mobile entity localization and tracking in GPS-less environments
Note: A sufficient connectivity condition for generic rigidity in the plane
Discrete Applied Mathematics
Operations preserving the global rigidity of graphs and frameworks in the plane
Computational Geometry: Theory and Applications
An Interlaced Extended Kalman Filter for sensor networks localisation
International Journal of Sensor Networks
Fully Decentralized, Collaborative Multilateration Primitives for Uniquely Localizing WSNs
WASA '09 Proceedings of the 4th International Conference on Wireless Algorithms, Systems, and Applications
Rigid tensegrity labelings of graphs
European Journal of Combinatorics
Rigid realizations of graphs on small grids
Computational Geometry: Theory and Applications
Globally rigid circuits of the direction--length rigidity matroid
Journal of Combinatorial Theory Series B
Sequential localization with inaccurate measurements
ACC'09 Proceedings of the 2009 conference on American Control Conference
Fully decentralized and collaborative multilateration primitives for uniquely localizing WSNs
EURASIP Journal on Wireless Communications and Networking - Special issue on wireless network algorithms, systems, and applications
Graphical properties of easily localizable sensor networks
Wireless Networks
Rigidity, global rigidity, and graph decomposition
European Journal of Combinatorics
An as-rigid-as-possible approach to sensor network localization
ACM Transactions on Sensor Networks (TOSN)
Beyond triangle inequality: sifting noisy and outlier distance measurements for localization
INFOCOM'10 Proceedings of the 29th conference on Information communications
Universal rigidity: towards accurate and efficient localization of wireless networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
Understanding node localizability of wireless ad-hoc networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
Generically globally rigid zeolites in the plane
Information Processing Letters
Rigidity guided localisation for mobile robotic sensor networks
International Journal of Ad Hoc and Ubiquitous Computing
Sensor network localization using sensor perturbation
ACM Transactions on Sensor Networks (TOSN)
Minimum cost localization problem in wireless sensor networks
Ad Hoc Networks
Formal Theory of Noisy Sensor Network Localization
SIAM Journal on Discrete Mathematics
Uniqueness of Low-Rank Matrix Completion by Rigidity Theory
SIAM Journal on Matrix Analysis and Applications
Beyond trilateration: on the localizability of wireless ad hoc networks
IEEE/ACM Transactions on Networking (TON)
Universal Rigidity and Edge Sparsification 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
Efficient algorithms for network localization using cores of underlying graphs
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
Encounter based sensor tracking
Proceedings of the thirteenth ACM international symposium on Mobile Ad Hoc Networking and Computing
Source location with rigidity and tree packing requirements
Operations Research Letters
Deriving Finite Sphere Packings
SIAM Journal on Discrete Mathematics
Highly connected rigidity matroids have unique underlying graphs
European Journal of Combinatorics
Beyond triangle inequality: Sifting noisy and outlier distance measurements for localization
ACM Transactions on Sensor Networks (TOSN)
Engineering Applications of Artificial Intelligence
Time-bounded essential localization for wireless sensor networks
IEEE/ACM Transactions on Networking (TON)
Generic global rigidity of body-bar frameworks
Journal of Combinatorial Theory Series B
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A d-dimensional framework is a straight line realization of a graph G in Rd. We shall only consider generic frameworks, in which the co-ordinates of all the vertices of G are algebraically independent. Two frameworks for G are equivalent if corresponding edges in the two frameworks have the same length. A framework is a unique realization of G in Rd if every equivalent framework can be obtained from it by an isometry of Rd. Bruce Hendrickson proved that if G has a unique realization in Rd then G is (d+1)-connected and redundantly rigid. He conjectured that every realization of a (d+1)-connected and redundantly rigid graph in Rd is unique. This conjecture is true for d = 1 but was disproved by Robert Connelly for d ≥ 3. We resolve the remaining open case by showing that Hendrickson's conjecture is true for d = 2. As a corollary we deduce that every realization of a 6-connected graph as a two-dimensional generic framework is a unique realization. Our proof is based on a new inductive characterization of 3-connected graphs whose rigidity matroid is connected.