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• W2014339452 abstract "Recently, Connelly and Sloughter [14] have introduced the notion of d-realizability of graphs and have, among other things, given a complete characterization of the class of 3-realizable graphs. However, their work has left open the question of finding an algorithm for realizing those graphs. In this paper, we resolve that question by showing that the semidefinite programming (SDP) approach of [11, 32] can be used for realizing 3-realizable graphs. Specifically, we use SDP duality theory to show that given a graph G and a set of lengths on its edges, the optimal dual multipliers of a certain SDP give rise to a proper equilibrium stress for some realization of G. Using this result and the techniques in [14, 31], we then obtain a polynomial time algorithm for (approximately) realizing 3-realizable graphs. Our results also establish a little-explored connection between SDP and tensegrity theories and allow us to derive some interesting properties of tensegrity frameworks." @default.
• W2014339452 created "2016-06-24" @default.
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• W2014339452 date "2006-01-22" @default.
• W2014339452 modified "2023-09-23" @default.
• W2014339452 title "A semidefinite programming approach to tensegrity theory and realizability of graphs" @default.
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• W2014339452 doi "https://doi.org/10.5555/1109557.1109641" @default.
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