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If a set K of nodes in a wireless network want to set up a routing structure that allows them to communicate with each other, one possible approach is to use a Steiner tree that spans all the nodes in K. However, a tree can be disconnected by the failure of a single link, and so it is desirable to employ other routing structures that are fault-tolerant. Furthermore, many real-world wireless networks are heterogeneous, meaning that the suitability of nodes for inclusion in the routing structure varies significantly. Therefore, it is meaningful to assign weights to the nodes and aim to compute a fault-tolerant routing structure of minimum total weight. In this paper, we model this problem as the problem of computing a minimum-weight 2-edge-connected Steiner subgraph spanning a given set of terminals, and we propose a constant-factor approximation algorithm for this problem in wireless networks that are modelled as unit disk graphs or quasi unit disk graphs.

Approximating fault-tolerant Steiner subgraphs in heterogeneous wireless networks