In a recent paper, combinatorial designs were used to construct switch-centric data centre networks that compare favourably with the ubiquitous (enhanced) fat-tree data centre networks in terms of the number of servers within (given a fixed server-to-server diameter). Unfortunately there were flaws in some of the proofs in that paper. We correct these flaws here and extend the results so as to prove that the core combinatorial construction, namely the 3-step construction, results in data centre networks with optimal path diversity.
Stewart, I. (2015). On the mathematics of data centre network topologies. In A. Kosowski, & I. Walukiewicz (Eds.), Fundamentals of computation theory : 20th international symposium, FCT 2015, Gdańsk, Poland, August 17 - 19, 2015 ; proceedings (283-295). https://doi.org/10.1007/978-3-319-22177-9_22