Connected rigidity matroids and unique realizations of graphs

By Bill Jackson, T. Jordán. J. Comb. Theory B, 2005

425 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computer Graphics and Computer-Aided Design, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/2c0a83bc685447b27b096654111ba15fb6cd3bbb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Computer Graphics and Computer-Aided Design

In Mechanical Engineering

Citations in the corpus

Theory of semidefinite programming for Sensor Network Localization (2005, background): “A recent result of JacksonandJordán[22] shows that inﬁnitesimal rigidity, three-connectivity and redundant rigidity are necessary and sufﬁcient conditions for unique realization of a graph in R 2 .”
Mobile-assisted localization in wireless sensor networks (2005, background): “However, Hendrickson conjectured that these two properties exactly characterize generic global rigidity in 2D, and this conjecture was recently proved in unpublished work of Jackson and Jordán [18].”
Notes on the Rigidity of Graphs (2007, background): “They are a combination of results from Berg and Jordán [2] and Jackson and Jordán [15].”
Location, Localization, and Localizability (2010, background): “Previous studies have shown that the network localizability problem is closely related to graph rigidity[69-72].”
Euclidean Distance Geometry and Applications (2012, background): “It was shown in [98, 45] that G is globally rigid for K = 2 if and only if either G is the 2-clique or 3-clique, or G is 3-connected and redundantly rigid.”
Rigidity, computation, and randomization in network localization (2004, background): “Theorem 6 ( [ 15 ]): A graph G with n ≥ 4 vertices is generically globally rigid in IR 2 if and only if it is 3-connected and redundantly rigid in IR 2.”
A Theory of Network Localization (2006, methodology): “In this paper, we have drawn on techniques and results from the first two fields, also combined in some previous joint work [21], as well as specific results on global rigidity [13], [34].”
The Cricket indoor location system (2005, background): “Hendrickson conjectured that above two properties exactly characterize generic global rigidity in 2D, and this conjecture was recently proved by Jackson and Jordán [52].”
Semidefinite Programming Approaches for Sensor Network Localization With Noisy Distance Measurements (2006, background): “Second, even if the distance measurements are perfectly accurate, a sufficient condition for this sensor network to be localizable cannot be identified easily [12], [13].”
Rigid graph control architectures for autonomous formations (2008, methodology): “Two sets of operations are discussed in [17] and [21].”