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.
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Acknowledgements
Project no. NKFI-128673 has been implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the FK_18 funding scheme. The first author was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences and by the ÚNKP-19-4 and ÚNKP-20-5 New National Excellence Program of the Ministry for Innovation and Technology. The second author was supported by the European Union, co-financed by the European Social Fund (EFOP-3.6.3-VEKOP-16-2017-00002). The authors are grateful to Tibor Jordán for his help, the inspiring discussions and his comments.
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Király, C., Mihálykó, A. (2021). Globally Rigid Augmentation of Minimally Rigid Graphs in \(\mathbb {R}^2\). In: Calamoneri, T., Corò, F. (eds) Algorithms and Complexity. CIAC 2021. Lecture Notes in Computer Science(), vol 12701. Springer, Cham. https://doi.org/10.1007/978-3-030-75242-2_23
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