The Bottleneck Biconnected Steiner Network Problem∗

We present the first exact algorithm for constructing minimum bottleneck 2-connected Steiner networks containing at most k Steiner points, where k > 2 is a constant integer. Given a set of n terminals embedded in the Euclidean plane, the objective of the problem is to find the locations of the Steiner points, and the topology of a 2-connected graph Nk spanning the Steiner points and the terminals, such that the length of the bottleneck (the longest edge of Nk) is minimised. The problem is motivated by the modelling of relay-augmentation for optimisation of energy consumption in survivable wireless communication networks. Our algorithm employs Voronoi diagrams and properties of block cut-vertex decompositions of graphs to find an optimal solution in O(h(k)nk log5k−1 n) steps, where h(k) is a function of k only.