k-Connectivity in Random Key Graphs with Unreliable Links

Random key graphs form a class of random intersection graphs and are naturally induced by the random key predistribution scheme of Eschenauer and Gligor for securing wireless sensor network (WSN) communications. Random key graphs have received much interest recently, owing in part to their wide applicability in various domains including recommender systems, social networks, secure sensor networks, clustering and classification analysis, and cryptanalysis to name a few. In this paper, we study connectivity properties of random key graphs in the presence of unreliable links. Unreliability of the edges are captured by independent Bernoulli random variables, rendering edges of the graph to be on or off independently from each other. The resulting model is an intersection of a random key graph and an Erdos-Renyi graph, and is expected to be useful in capturing various real-world networks; e.g., with secure WSN applications in mind, link unreliability can be attributed to harsh environmental conditions severely impairing transmissions. We present conditions on how to scale this model's parameters so that i) the minimum node degree in the graph is at least k, and ii) the graph is k-connected, both with high probability as the number of nodes becomes large. The results are given in the form of zeroone laws with critical thresholds identified and shown to coincide for both graph properties. These findings improve the previous results by Rybarczyk on the k-connectivity of random key graphs (with reliable links), as well as the zero-one laws by Yagan on the 1-connectivity of random key graphs with unreliable links.Comment: Published in IEEE Transactions on Information Theor

On Topological Properties of Wireless Sensor Networks under the q-Composite Key Predistribution Scheme with On/Off Channels

The q-composite key predistribution scheme [1] is used prevalently for secure communications in large-scale wireless sensor networks (WSNs). Prior work [2]-[4] explores topological properties of WSNs employing the q-composite scheme for q = 1 with unreliable communication links modeled as independent on/off channels. In this paper, we investigate topological properties related to the node degree in WSNs operating under the q-composite scheme and the on/off channel model. Our results apply to general q and are stronger than those reported for the node degree in prior work even for the case of q being 1. Specifically, we show that the number of nodes with certain degree asymptotically converges in distribution to a Poisson random variable, present the asymptotic probability distribution for the minimum degree of the network, and establish the asymptotically exact probability for the property that the minimum degree is at least an arbitrary value. Numerical experiments confirm the validity of our analytical findings.Comment: Best Student Paper Finalist in IEEE International Symposium on Information Theory (ISIT) 201

Research on Wireless Multi-hop Networks: Current State and Challenges

Wireless multi-hop networks, in various forms and under various names, are being increasingly used in military and civilian applications. Studying connectivity and capacity of these networks is an important problem. The scaling behavior of connectivity and capacity when the network becomes sufficiently large is of particular interest. In this position paper, we briefly overview recent development and discuss research challenges and opportunities in the area, with a focus on the network connectivity.Comment: invited position paper to International Conference on Computing, Networking and Communications, Hawaii, USA, 201

k-connectivity of Random Graphs and Random Geometric Graphs in Node Fault Model

k-connectivity of random graphs is a fundamental property indicating reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of sensor nodes with limited power resources are modeled by random graphs with unreliable nodes, which is known as the node fault model. In this paper, we investigate k-connectivity of random graphs in the node fault model by evaluating the network breakdown probability, i.e., the disconnectivity probability of random graphs after stochastic node removals. Using the notion of a strongly typical set, we obtain universal asymptotic upper and lower bounds of the network breakdown probability. The bounds are applicable both to random graphs and to random geometric graphs. We then consider three representative random graph ensembles: the Erdos-Renyi random graph as the simplest case, the random intersection graph for WSNs with random key predistribution schemes, and the random geometric graph as a model of WSNs generated by random sensor node deployment. The bounds unveil the existence of the phase transition of the network breakdown probability for those ensembles.Comment: 6 page

Node counting in wireless ad-hoc networks

We study wireless ad-hoc networks consisting of small microprocessors with limited memory, where the wireless communication between the processors can be highly unreliable. For this setting, we propose a number of algorithms to estimate the number of nodes in the network, and the number of direct neighbors of each node. The algorithms are simulated, allowing comparison of their performance

The impact of mobility models on the performance of mobile Ad Hoc network routing protocol

A mobility model represents nodes distribution and movement over the network. Several research works have shown that a selection of mobility model can affect the outcome of routing performance simulation in Mobile Ad Hoc Networks. Thus, a routing protocol may only be effective in a particular mobility model or scenario but performs inferiorly in another. As a result, analyses of routing protocol performance are often based on inadequate information leading to inaccurate argument and conclusion. In this paper, three different mobility models have been selected, where each of them is highly distinctive in terms of nodes movement behavior. In addition, a new measurement technique called probability of route connectivity is introduced. The technique is used to quantify the success rate of route established by a routing protocol. Extensive simulation runs are done and results are compared between each mobility model

1-D Coordinate Based on Local Information for MAC and Routing Issues in WSNs

More and more critical Wireless Sensor Networks (WSNs) applications are emerging. Those applications need reliability and respect of time constraints. The underlying mechanisms such as MAC and routing must handle such requirements. Our approach to the time constraint problem is to bound the hop-count between a node and the sink and the time it takes to do a hop so the end-to-end delay can be bounded and the communications are thus real-time. For reliability purpose we propose to select forwarder nodes depending on how they are connected in the direction of the sink. In order to be able to do so we need a coordinate (or a metric) that gives information on hop-count, that allows to strongly differentiate nodes and gives information on the connectivity of each node keeping in mind the intrinsic constraints of WSWs such as energy consumption, autonomy, etc. Due to the efficiency and scalability of greedy routing in WSNs and the financial cost of GPS chips, Virtual Coordinate Systems (VCSs) for WSNs have been proposed. A category of VCSs is based on the hop-count from the sink, this scheme leads to many nodes having the same coordinate. The main advantage of this system is that the hops number of a packet from a source to the sink is known. Nevertheless, it does not allow to differentiate the nodes with the same hop-count. In this report we propose a novel hop-count-based VCS which aims at classifying the nodes having the same hop-count depending on their connectivity and at differentiating nodes in a 2-hop neighborhood. Those properties make the coordinates, which also can be viewed as a local identifier, a very powerful metric which can be used in WSNs mechanisms.Comment: (2011