Enumerating Non-crossing Minimally Rigid Frameworks

  • David Avis
  • Naoki Katoh
  • Makoto Ohsaki
  • Ileana Streinu
  • Shin-ichi Tanigawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)

Abstract

In this paper we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid bar-and-joint frameworks (simply called non-crossing Laman frameworks) on a given generic set of n points. Our algorithm is based on the reverse search paradigm of Avis and Fukuda. It generates each output graph in O(n 4) time and O(n) space, or, with a slightly different implementation, in O(n 3) time and O(n 2) space. In particular, we obtain that the set of all non-crossing Laman frameworks on a given point set is connected by flips which remove an edge and then restore the Laman property with the addition of a non-crossing edge.

Keywords

Search Tree Parent Function Outer Face Rigid Framework Rigid Component 
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 2006

Authors and Affiliations

  • David Avis
    • 1
  • Naoki Katoh
    • 2
  • Makoto Ohsaki
    • 2
  • Ileana Streinu
    • 3
  • Shin-ichi Tanigawa
    • 2
  1. 1.School of Computer ScienceMcGill UniversityCanada
  2. 2.Department of Architecture and Architectural EngineeringKyoto UniversityKyotoJapan
  3. 3.Dept. of Comp. ScienceSmith CollegeNorthamptonUSA

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