The paper "Computing branchwidth via efficient triangulations and blocks" by Fedor V. Fomin, Frédéric Mazoit, and Ioan Todinca presents an efficient algorithm for computing the branchwidth of a graph. The authors build upon the concept of minimal triangulations and potential maximal cliques, which are crucial for polynomial-time algorithms on graph classes to compute treewidth. They introduce the notions of efficient triangulations and blocks, which serve as the main ingredients for their algorithm. Efficient triangulations are chordal graphs that respect the minimal separators of the original graph, while blocks are sets of vertices whose neighborhoods form minimal separators. The paper demonstrates how these structures can be used to construct an algorithm that computes the branchwidth of a graph in time \((2 + \sqrt{3})^n \cdot n^{O(1)}\). This is the fastest known exact algorithm for computing branchwidth, outperforming previous exponential-time algorithms. The authors also provide a detailed proof of their main theorem and discuss potential improvements and open problems in the field.The paper "Computing branchwidth via efficient triangulations and blocks" by Fedor V. Fomin, Frédéric Mazoit, and Ioan Todinca presents an efficient algorithm for computing the branchwidth of a graph. The authors build upon the concept of minimal triangulations and potential maximal cliques, which are crucial for polynomial-time algorithms on graph classes to compute treewidth. They introduce the notions of efficient triangulations and blocks, which serve as the main ingredients for their algorithm. Efficient triangulations are chordal graphs that respect the minimal separators of the original graph, while blocks are sets of vertices whose neighborhoods form minimal separators. The paper demonstrates how these structures can be used to construct an algorithm that computes the branchwidth of a graph in time \((2 + \sqrt{3})^n \cdot n^{O(1)}\). This is the fastest known exact algorithm for computing branchwidth, outperforming previous exponential-time algorithms. The authors also provide a detailed proof of their main theorem and discuss potential improvements and open problems in the field.