As the development of distributed systems progresses, more and more challenges arise and the need for developing optimized systems and for optimizing existing systems from multiple perspectives becomes more stringent. In this paper I present novel algorithmic techniques for solving several optimization problems regarding distributed systems with tree topologies. I address topics like: reliability improvement, partitioning, coloring, content delivery, optimal matchings, as well as some tree counting aspects. Some of the presented techniques are only of theoretical interest, while others can be used in practical settings.