Exact algorithm for the bottleneck 2-connected $k$-Steiner network problem

Details Exact algorithm for the bottleneck 2-connected $k$-Steiner network problem Exact algorithm for the bottleneck 2-connected $k$-Steiner network problem

2011-11-09

arxiv.org/abs/1111.2105v1

Mathematics

Metric Geometry

Scientific paper

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. The objective of the problem is -- given a set of $n$ terminals embedded in the Euclidean plane -- 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 motivated by the modelling of relay-augmentation for optimisation of energy consumption in wireless transmission 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.

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