Appendix overview

The appendix is subdivided into the following seven topics: A Central angle property: Quick proof of the central angle property, used in Sect. B Optimal Land V-shaped branching: Derivation of the conditions listed in Tab. 1 under which V-or L-branching are optimal. E Non-optimality of higher-degree branchings: Technical proofs and numerical scheme to show the non-optimality of higher-degree branchings discussed in Sect. F BOT on two-dimensional Riemannian manifolds: Formal proof of Theorem 5.1, which generalizes the optimal branching conditions and other properties from the Euclidean plane to embedded surfaces. A sketch of the proof can be found in Sect. G Algorithms: Additional details and experiments for the different algorithms presented in the main paper. Section G.2 focuses on the numerical geometry optimization and Sect. Section G.1 holds a few examples of the recursive geometric construction of relatively optimal solutions for BOT problems with multiple sources. In this section, we present a geometric proof of the central angle property used in the geometric construction of relatively optimal solutions for a given full tree topology (see Sect. 3.2). Below, we formally derive the conditions listed in Tab. 1 under which V-or L-branching provide the optimal solution to a BOT problem with one source and two sinks.