Worst-case ratios of networks in the rectilinear plane

For point sets in the rectilinear plane we consider the following five measures of the interconnect length and prove bounds on the worst-case ratio: minimum Steiner tree, minimum star, clique, minimum spanning tree, and bounding box. In particular, we prove that for any set of n points: (n − 1) times the shortest Steiner tree is less or equal to the clique unless n = 4; and the minimum spanning tree is less or equal to the shortest star unless n ∈ {3, 4, 5}.