This version of FAµST adds the binary balanced tree implementation of the butterfly hierarchical factorization. As you can see in the following figure it speeds up the factorization about a factor of two compared to right/left hierarchical factorization.
Reference: Léon Zheng, Elisa Riccietti, Rémi Gribonval. Hierarchical Identifiability in Multilayer Sparse Matrix Factorization. 2021. ⟨hal-03362626v2⟩