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On stress matrices of (d + 1)-lateration frameworks in general position

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Abstract

Let (G, P) be a bar framework of n vertices in general position in \({\mathbb{R}^d}\) , for dn − 1, where G is a (d + 1)-lateration graph. In this paper, we present a constructive proof that (G, P) admits a positive semidefinite stress matrix with rank (nd − 1). We also prove a similar result for a sensor network, where the graph consists of m(≥ d + 1) anchors.

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Correspondence to Nicole Taheri.

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Alfakih’s research is supported by the Natural Sciences and Engineering Research Council of Canada. Taheri’s research is supported in part by DOE Grant DE-SC0002009. Ye’s research supported in part by NSF Grant GOALI 0800151 and DOE Grant DE-SC0002009. This paper is a shortened version of [7].

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Alfakih, A.Y., Taheri, N. & Ye, Y. On stress matrices of (d + 1)-lateration frameworks in general position. Math. Program. 137, 1–17 (2013). https://doi.org/10.1007/s10107-011-0480-0

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  • DOI: https://doi.org/10.1007/s10107-011-0480-0

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