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 N k spanning the Steiner points and the terminals, such that the length of the bottleneck (the longest edge of N k) is minimised. The problem is

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... vated by the modelling of relay-augmentation for optimisation of energy consumption in sur-vivable 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) n k log 5k−1 n) steps, where h(k) is a function of k only.