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- W171846763 abstract "A configuration p in r-dimensional Euclidean space is a finite collection of labeled points $${p}^{1},ldots ,{p}^{n}$$ in $${mathbb{R}}^{r}$$ that affinely span $${mathbb{R}}^{r}$$ . Each configuration p defines a Euclidean distance matrix $${D}_{p} = ({d}_{ij})$$ = $$(vert vert {p}^{i} - {p}^{j}vert {vert }^{2})$$ , where $$vert vert cdot vert vert $$ denotes the Euclidean norm. A fundamental problem in distance geometry is to find out whether or not a given proper subset of the entries of D p suffices to uniquely determine the entire matrix D p . This problem is known as the universal rigidity problem of bar frameworks. In this chapter, we present a unified approach for the universal rigidity of bar frameworks, based on Euclidean distance matrices (EDMs), or equivalently, on projected Gram matrices. This approach makes the universal rigidity problem amenable to semidefinite programming methodology. Using this approach, we survey some recently obtained results and their proofs, emphasizing the case where the points $${p}^{1},ldots ,{p}^{n}$$ are in general position." @default.
- W171846763 created "2016-06-24" @default.
- W171846763 creator A5061388681 @default.
- W171846763 date "2012-11-03" @default.
- W171846763 modified "2023-09-26" @default.
- W171846763 title "Universal Rigidity of Bar Frameworks in General Position: A Euclidean Distance Matrix Approach" @default.
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- W171846763 doi "https://doi.org/10.1007/978-1-4614-5128-0_1" @default.
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