A Henneberg-based algorithm for generating tree-decomposable minimally rigid graphs

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...

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Bibliographic Details
Authors: Hidalgo, MR, Joan-Arinyo, R
Format: article
Status:Published version
Publication Date:2017
Country:España
Institution:Fundación para el Fomento de la Investigación Sanitaria y Biomédica de la Comunitat Valenciana (FISABIO)
Repository:r-FISABIO. Repositorio Institucional de Producción Científica
OAI Identifier:oai:fisabio.fundanetsuite.com:p13038
Online Access:https://fisabio.portalinvestigacion.com/publicaciones/13038
Access Level:Open access
Keyword:Minimally rigid graphs
Laman graphs
Henneberg sequences
Geometric constraint solving
Geometric constraint graphs
Tree-decomposition
Description
Summary: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 (vertical bar V vertical bar(3)). (C) 2016 Elsevier Ltd. All rights reserved.