What are examples of applications of the tree decomposition of a graph? I am looking for specific applications of the tree decomposition (of a graph), because I want to motivate its existence. What are examples of problems that are more easily solvable using the junction tree of a graph (rather than tackling the problem directly on the graph)? Please, provide also the references to the papers or books that mention these specific applications.
An example of an application of the junction tree (or tree decomposition) of graph is described in the paper Junction Tree Variational Autoencoder for Molecular Graph Generation (2019), by Wengong Jin, Regina Barzilay and Tommi Jaakkola.