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Enumerating Planar Minimally Rigid Graphs David Avis1, Naoki Katoh2 , Makoto Ohsaki2,
 

Summary: Enumerating Planar Minimally Rigid Graphs
David Avis1, Naoki Katoh2 , Makoto Ohsaki2,
Ileana Streinu3 , and Shin-ichi Tanigawa2
1
School of Computer Science, McGill University, Canada. avis@cs.macgill.ca
2
Department of Architecture and Architectural Engineering, Kyoto University, Kyoto 615-8450 Japan,
ohsaki,naoki,is.tanigawa@archi.kyoto-u.ac.jp.
3
Dept. of Comp. Science, Smith College,Northampton, MA 01063, USA, streinu@cs.smith.edu.
Abstract. We present an algorithm for enumerating without repetitions all the planar (non-
crossing) minimally rigid (Laman) graphs embedded 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(n4
) time and O(n) space, or, with a slightly different implementation, in
O(n3
) time and O(n2
) space.
In particular, we obtain that the set of all planar Laman graphs on a given point set is
connected by flips which remove an edge and then restore the Laman property with the

  

Source: Avis, David - School of Computer Science, McGill University

 

Collections: Computer Technologies and Information Sciences