In the dynamic tree problem the goal is the maintenance of an arbitrary n-vertex forest, where the trees are subject to joining and splitting by, respectively, adding and removing edges. Depending on the application, information can be associated to nodes or edges (or both), and queries might require to combine values in path or (sub)trees. In this paper we present a novel data structure, called the Depth First Tour Tree, based on a linearization of a DFS visit of the tree. Despite the simplicity of the approach, similar to the ET-Trees (based on a Euler Tour), our data structure is able to answer queries related to both paths and (sub)trees. In particular, focusing on subtree computations, we show how to customize the data structure in order to answer queries for a concrete application: keeping track of the biconnectivity measures, including the impact of the removal of articulation points, of a dynamic undirected graph.
Farina, G., & Laura, L. (2016). Dynamic subtrees queries revisited: The Depth First Tour Tree. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9538, pp. 148–160). Springer Verlag. https://doi.org/10.1007/978-3-319-29516-9_13