Abstract
Let \({\mathcal R}_{d}(G)\) be the d-dimensional rigidity matroid for a graph G=(V,E). Combinatorial characterization of generically rigid graphs is known only for the plane d=2 [11]. Recently Jackson and Jordán [5] derived a min-max formula which determines the rank function in \({\mathcal R}_{d}(G)\) when G is sparse, i.e. has maximum degree at most d + 2 and minimum degree at most d + 1.
We present three efficient algorithms for sparse graphs G that
(i) detect if E is independent in the rigidity matroid for G, and
(ii) construct G using vertex insertions preserving if G is isostatic, and
(iii) compute the rank of \({\mathcal R}_{d}(G)\).
The algorithms have linear running time assuming that the dimension d is fixed.
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Bereg, S. (2005). Algorithms for the d-Dimensional Rigidity Matroid of Sparse Graphs. In: Akiyama, J., Kano, M., Tan, X. (eds) Discrete and Computational Geometry. JCDCG 2004. Lecture Notes in Computer Science, vol 3742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11589440_3
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DOI: https://doi.org/10.1007/11589440_3
Publisher Name: Springer, Berlin, Heidelberg
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