A Henneberg-based algorithm for generating tree-decomposable minimally rigid graphs. (March 2017)

• Record Type: Journal Article
• Authors: Hidalgo, Marta R.; Joan-Arinyo, Robert
• Is Part Of: Journal of symbolic computation. Volume 79(2017)Part 2
• Page Start: 232
• Page End: 248
• Publication Date: 2017-03
• Subjects: Minimally rigid graphs -- Laman graphs -- Henneberg sequences -- Geometric constraint solving -- Geometric constraint graphs -- Tree-decomposition; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.02.006
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this work we describe an algorithm to generate tree-decomposable minimally rigid graphs on a given set of vertices V . The main idea is based on the well-known fact that all minimally rigid graphs, also known as Laman graphs, can be generated via Henneberg sequences. Given that not each minimally rigid graph is tree-decomposable, we identify a set of conditions on the way Henneberg steps are applied so that the resulting graph is tree-decomposable. We show that the worst case running time of the algorithm is O ( | V | 3 ) .