2006/08/03 by David Avis, Avis, David, Naoki Katoh +7 · 1 citation
Computer Science · Engineering · #68W01 #Advanced Materials and Mechanics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.math/0608102
openalex publication_date 2006/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid bar-and-joint frameworks under edge constraints (also called constrained 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(n4) time and O(n) space, or, slightly different implementation, in O(n3) time and O(n2) space. In particular, we obtain that the set of all the constrained non-crossing Laman frameworks on a given point set is connected by flips which restore the Laman property.