Globally Rigid Augmentation of Minimally Rigid Graphs in $$\mathbb {R}^2$$ | SpringerLink
The two main concepts of Rigidity Theory are rigidity, where the framework has no continuous deformation, and global rigidity, where the given distance set determines the locations of the points up to isometry. We consider the following augmentation problem....
Abstract The two main concepts of Rigidity Theory are rigidity, where the framework has no continuous deformation, and global rigidity, where the given distance set determines the locations of the points up to isometry. We consider the following augmentation problem. Given a minimally rigid graph \(G=(V,E)\) in \(\mathbb {R}^2\) , find a minimum cardinality edge set F such that the graph \(G'=(V,E+F)\) is globally rigid in \(\mathbb {R}^2\) . We provide a min-max theorem and an \(O(|V|^2)\) time algorithm for this problem. This is a preview of subscription content, log in via an institution to
related reading
- Why is this graph not generically globally rigid? - MathOverflowmathoverflow.net
- Uniquely Localizable Networks with Few Anchors | Springer Nature Linklink.springer.com
- Modular Manifolds - Thinking Machines Labthinkingmachines.ai
- Sublinear expandersias.edu
- Ch12.pdfmath.uni-hamburg.de
- [1605.08101] Global rates of convergence for nonconvex optimization on manifoldsarxiv.org
- Ramsey theory and strength of graphsarxiv.org
- Exact Stability for Turan's Theoremarxiv.org
- A simpler proof of the KPR theorem | tcs mathtcsmath.wordpress.com
- Expander graph - Wikipediaen.wikipedia.org
- [2309.10122] Graph Threadingarxiv.org
- Understanding Convolutions on Graphsdistill.pub