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Algorithms for the d-Dimensional Rigidity Matroid of Sparse Graphs

  • Sergey Bereg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3742)

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.

Keywords

Linear Time Connected Graph Rank Function Sparse Graph Rigidity Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sergey Bereg
    • 1
  1. 1.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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