Consider a placement of heterogeneous, wireless sensors that can vary the transmission range by increasing or decreasing power. The problem of determining an optimal assignment of transmission radii, so that the resulting network is strongly-connected and more generally k-connected has been studied in the literature. In traditional k-connectedness, the network is able resist the failure of up to k - 1 nodes anywhere in the network, and still remain strongly-connected. In this paper we introduce a much stronger k-connectedness property, which we show can be implemented efficiently, and without great increase in the radii of transmission needed to simply achieve connectedness. We say that a network is dominating kconnected if, for any simultaneous failure of nodes throughout the network, with at most k - 1 nodes failures occurring in the out-neighborhood any surviving (up) node, the set U of up nodes forms a dominating set and induces a strongly-connected subdigraph. In this paper, we gi...
Kenneth A. Berman, Fred S. Annexstein, Aravind Ran