on Information Theory

Paper ID | G.1.5 | ||

Paper Title | k-Connectivity in Random Graphs induced by Pairwise Key Predistribution Schemes |
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Authors | Mansi Sood, Osman Yagan, Carnegie Mellon University Pittsburgh, United States | ||

Session | G.1: Graph Analytics | ||

Presentation | Lecture | ||

Track | Graphs, Games, Sparsity, and Signal Processing |
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Manuscript | Click here to download the manuscript | ||

Virtual Presentation | Click here to watch in the Virtual Symposium | ||

Abstract | Random key predistribution schemes serve as a viable solution for facilitating secure communication in Wireless Sensor Networks (WSNs). We analyze \emph{reliable} connectivity of a {\em heterogeneous} WSN under the random pairwise key predistribution scheme of Chan et al. According to this scheme, each of the $n$ sensor nodes is classified as type-1 (respectively, type-2) with probability $\mu$ (respectively, $1-\mu)$ where $0<\mu<1$. Each type-1 (respectively, type-2) node is {\em paired} with 1 (respectively, $K_n$) other node selected uniformly at random; each {\em pair} is then assigned a unique pairwise key so that they can securely communicate with each other. A main question in the design of secure and heterogeneous WSNs is how should the parameters $n$, $\mu$, and $K_n$ be selected such that resulting network exhibits certain desirable properties with high probability. Of particular interest is the {\em strength} of connectivity often studied in terms of $k$-connectivity; i.e., with $k=1, 2, \ldots$, the property that the network remains connected despite the removal of any $k-1$ nodes or links.In this paper, we answer this question by analyzing the {\em inhomogeneous random K-out graph} model naturally induced under the heterogeneous pairwise scheme. It was recently established that this graph is 1-connected asymptotically almost surely (a.a.s.) if and only if $K_n=\omega(1)$. Here, we show that for $k=2, 3, \ldots$, we need to set $K_n = \frac{1}{1-\mu}(\log n +(k-2)\log\log n + \omega(1))$ for the network to be $k$-connected a.a.s. The result is given in the form of a zero-one law indicating that the network is a.a.s. {\em not} $k$-connected when $K_n = \frac{1}{1-\mu}(\log n +(k-2)\log\log n - \omega(1))$. We present simulation results to demonstrate the usefulness of the results in the finite node regime. |

Plan Ahead

2021 IEEE International Symposium on Information Theory

**11-16 July 2021 ** | **Melbourne, Victoria, Australia**