A Henneberg-based algorithm for generating tree-decomposable minimally rigid graphs
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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).
CitationHidalgo, M., Joan-Arinyo, R. A Henneberg-based algorithm for generating tree-decomposable minimally rigid graphs. "Journal of symbolic computation", 1 Març 2017, vol. 79, Part 2, p. 232-248.