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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Detalles Bibliográficos
Autores: Hidalgo, Marta R., Joan Arinyo, Robert|||0000-0002-1896-2940
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/102162
Acceso en línea:https://hdl.handle.net/2117/102162
https://dx.doi.org/10.1016/j.jsc.2016.02.006
Access Level:acceso abierto
Palabra clave:Graph algorithms
Minimally rigid graphs
Laman graphs
Henneberg sequences
Geometric constraint solving
Geometric constraint graphs
Tree-decomposition
Algorismes de grafs
Àrees temàtiques de la UPC::Informàtica
Descripción
Sumario: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).