adv

Connectivity of inhomogeneous random K-out graphs. (arXiv:1810.09921v1 [math.CO])

We investigate the connectivity of wireless sensor networks secured by the heterogeneous random pairwise key predistribution scheme. In contrast to the homogeneous scheme proposed by Chan et al., where each node is paired (offline) with $K$ other nodes chosen uniformly at random; herein, each node is classified as class-$1$ with probability $\mu$ or class-$2$ with probability $1-\mu$, for $0<\mu<1$, independently. Then, each class-$1$ (respectively, class-$2$) node is paired (offline) with $K_1$ (respectively, $K_2$) other nodes selected uniformly at random. We consider the particular case when $K_1=1$ and $K_2=K$. The heterogeneous random pairwise scheme induces an inhomogeneous random K-out graph $\mathbb{H} (n;\mu,K_n)$, where $n$ denotes the number of nodes and $K_n$ denotes a scaling of $K$ with respect to the network size $n$. Hence, establishing the connectivity of wireless sensor networks secured by the heterogeneous random pairwise scheme maps to deriving conditions on h查看全文

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