arXiv subjects

Osman Yağan

Publications and source records attributed to Osman Yağan.

At least 37 records · Page 2Linked to original sources

arXiv2017

Connectivity of Wireless Sensor Networks Secured by Heterogeneous Key Predistribution Under an On/Off Channel Model

We investigate the connectivity of a wireless sensor network secured by the heterogeneous key predistribution scheme under an independent on/off channel model. The heterogeneous scheme induces an inhomogeneous random key graph, denoted by $\mathbb{K}(n;\pmbμ,\pmb{K},P)$ and the on/off channel model induces an Erdős-Rényi graph, denoted by $\mathbb{H}(n,α)$. Hence, the overall random graph modeling the WSN is obtained by the intersection of $\mathbb{K}(n;\pmbμ,\pmb{K},P)$ and $\mathbb{H}(n,α)$. We present conditions on how to scale the parameters of the intersecting graph with respect to the network size $n$ such that the graph i) has no isolated nodes and ii) is connected, both with high probability as the number of nodes gets large. Our results are supported by a simulation study demonstrating that i) despite their asymptotic nature, our results can in fact be useful in designing finite-node wireless sensor networks so that they achieve secure connectivity with high probability; and ii) despite the simplicity of the on/off communication model, the probability of connectivity in the resulting wireless sensor network approximates very well the case where the disk model is used.

math.OC↗

arXiv2017

Counting triangles, tunable clustering and the small-world property in random key graphs (Extended version)

Random key graphs were introduced to study various properties of the Eschenauer-Gligor key predistribution scheme for wireless sensor networks (WSNs). Recently this class of random graphs has received much attention in contexts as diverse as recommender systems, social network modeling, and clustering and classification analysis. This paper is devoted to analyzing various properties of random key graphs. In particular, we establish a zero-one law for the the existence of triangles in random key graphs, and identify the corresponding critical scaling. This zero-one law exhibits significant differences with the corresponding result in Erdos-Renyi (ER) graphs. We also compute the clustering coefficient of random key graphs, and compare it to that of ER graphs in the many node regime when their expected average degrees are asymptotically equivalent. For the parameter range of practical relevance in both wireless sensor network and social network applications, random key graphs are shown to be much more clustered than the corresponding ER graphs. We also explore the suitability of random key graphs as small world models in the sense of Watts and Strogatz.

cs.SI↗

arXiv2016

Node Isolation of Secure Wireless Sensor Networks under a Heterogeneous Channel Model

We investigate the secure connectivity of wireless sensor networks under a heterogeneous random key predistribution scheme and a heterogeneous channel model. In particular, we study a random graph formed by the intersection of an inhomogeneous random key graph with an inhomogeneous Erdős-Rényi graph. The former graph is naturally induced by the heterogeneous random key predistribution scheme while the latter graph constitutes a heterogeneous on/off channel model; wherein, the wireless channel between a class-$i$ node and a class-$j$ node is on with probability $α_{ij}$ independently. We present conditions (in the form of zero-one laws) on how to scale the parameters of the intersection model so that it has no isolated node with high probability as the number of nodes gets large. We also present numerical results to support these zero-one laws in the finite-node regime.

cs.IT↗

arXiv2016

On the Network Reliability Problem of the Heterogeneous Key Predistribution Scheme

We consider the network reliability problem in wireless sensor networks secured by the heterogeneous random key predistribution scheme. This scheme generalizes Eschenauer-Gligor scheme by considering the cases when the network comprises sensor nodes with varying level of resources; e.g., regular nodes vs. cluster heads. The scheme induces the inhomogeneous random key graph, denoted $\mathbb{G}(n;\pmbμ,\pmb{K},P)$. We analyze the reliability of $\mathbb{G}(n;\pmbμ,\pmb{K},P)$ against random link failures. Namely, we consider $\mathbb{G}(n;\pmbμ,\pmb{K}, P,α)$ formed by deleting each edge of $\mathbb{G}(n;\pmbμ,\pmb{K},P)$ independently with probability $1-α$, and study the probability that the resulting graph i) has no isolated node; and ii) is connected. We present scaling conditions on $\pmb{K}$, $P$, and $α$ such that both events take place with probability zero or one, respectively, as the number of nodes gets large. We present numerical results to support these in the finite-node regime.

cs.IT↗

arXiv2016

$k$-connectivity of inhomogeneous random key graphs with unreliable links

We consider secure and reliable connectivity in wireless sensor networks that utilize a heterogeneous random key predistribution scheme. We model the unreliability of wireless links by an on-off channel model that induces an Erdős-Rényi graph, while the heterogeneous scheme induces an inhomogeneous random key graph. The overall network can thus be modeled by the intersection of both graphs. We present conditions (in the form of zero-one laws) on how to scale the parameters of the intersection model so that with high probability i) all of its nodes are connected to at least $k$ other nodes; i.e., the minimum node degree of the graph is no less than $k$ and ii) the graph is $k$-connected, i.e., the graph remains connected even if any $k-1$ nodes leave the network. We also present numerical results to support these conditions in the finite-node regime. Our results are shown to complement and generalize several previous work in the literature.

cs.CR↗

arXiv2016

Minimum node degree in inhomogeneous random key graphs with unreliable links

We consider wireless sensor networks under a heterogeneous random key predistribution scheme and an on-off channel model. The heterogeneous key predistribution scheme has recently been introduced by Yağan - as an extension to the Eschenauer and Gligor scheme - for the cases when the network consists of sensor nodes with varying level of resources and/or connectivity requirements, e.g., regular nodes vs. cluster heads. The network is modeled by the intersection of the inhomogeneous random key graph (induced by the heterogeneous scheme) with an Erdős-Rényi graph (induced by the on/off channel model). We present conditions (in the form of zero-one laws) on how to scale the parameters of the intersection model so that with high probability all of its nodes are connected to at least $k$ other nodes; i.e., the minimum node degree of the graph is no less than $k$. We also present numerical results to support our results in the finite-node regime. The numerical results suggest that the conditions that ensure $k$-connectivity coincide with those ensuring the minimum node degree being no less than $k$.

cs.CR↗

arXiv2016

Secure and reliable connectivity in heterogeneous wireless sensor networks

We consider wireless sensor networks secured by the heterogeneous random key predistribution scheme under an on/off channel model. The heterogeneous random key predistribution scheme considers the case when the network includes sensor nodes with varying levels of resources, features, or connectivity requirements; e.g., regular nodes vs. cluster heads, but does not incorporate the fact that wireless channel are unreliable. To capture the unreliability of the wireless medium, we use an on/off channel model; wherein, each wireless channel is either on (with probability $α$) or off (with probability $1-α$) independently. We present conditions (in the form of zero-one laws) on how to scale the parameters of the network model so that with high probability the network is $k$-connected, i.e., the network remains connected even if any $k-1$ nodes fail or leave the network. We also present numerical results to support these conditions in the finite-node regime.

cs.NI↗

arXiv2016

Clustering determines the dynamics of complex contagions in multiplex networks

We present the mathematical analysis of generalized complex contagions in clustered multiplex networks for susceptible-infected-recovered (SIR)-like dynamics. The model is intended to understand diffusion of influence, or any other spreading process implying a threshold dynamics, in setups of interconnected networks with significant clustering. The contagion is assumed to be general enough to account for a content-dependent linear threshold model, where each link type has a different weight (for spreading influence) that may depend on the content (e.g., product, rumor, political view) that is being spread. Using the generating functions formalism, we determine the conditions, probability, and expected size of the emergent global cascades. This analysis provides a generalization of previous approaches and is specially useful in problems related to spreading and percolation. The results present non trivial dependencies between the clustering coefficient of the networks and its average degree. In particular, several phase transitions are shown to occur depending on these descriptors. Generally speaking, our findings reveal that increasing clustering decreases the probability of having global cascades and their size, however this tendency changes with the average degree. There exists a certain average degree from which on clustering favours the probability and size of the contagion. By comparing the dynamics of complex contagions over multiplex networks and their monoplex projections, we demonstrate that ignoring link types and aggregating network layers may lead to inaccurate conclusions about contagion dynamics, particularly when the correlation of degrees between layers is high.

physics.soc-ph↗

arXiv2015

On the Eschenauer-Gligor key predistribution scheme under on-off communication channels: The absence of isolated nodes (Extended version)

We consider the Eschenauer-Gligor key predistribution scheme under the condition of partial visibility with i.i.d. on-off links between pairs of nodes. This situation is modeled as the intersection of two random graphs, namely a random key graph and an Erdős-Rényi (ER) graph. For this class of composite random graphs we give various improvements on a recent result by Yağan [IEEE Transactions on Information Theory, 58(6):3821-3835, 2012] concerning zero-one laws for the absence of isolated nodes.

math.PR↗

arXiv2015

Information Propagation in Clustered Multilayer Networks

In today's world, individuals interact with each other in more complicated patterns than ever. Some individuals engage through online social networks (e.g., Facebook, Twitter), while some communicate only through conventional ways (e.g., face-to-face). Therefore, understanding the dynamics of information propagation among humans calls for a multi-layer network model where an online social network is conjoined with a physical network. In this work, we initiate a study of information diffusion in a clustered multi-layer network model, where all constituent layers are random networks with high clustering. We assume that information propagates according to the SIR model and with different information transmissibility across the networks. We give results for the conditions, probability, and size of information epidemics, i.e., cases where information starts from a single individual and reaches a positive fraction of the population. We show that increasing the level of clustering in either one of the layers increases the epidemic threshold and decreases the final epidemic size in the whole system. An interesting finding is that information with low transmissibility spreads more effectively with a small but densely connected social network, whereas highly transmissible information spreads better with the help of a large but loosely connected social network.

physics.soc-ph↗

arXiv2015

Designing Securely and Reliably Connected Wireless Sensor Networks

In wireless sensor networks, the $q$-composite key predistribution scheme is a widely recognized way to secure communications. Although connectivity properties of secure sensor networks with the $q$-composite scheme have been studied in the literature, few results address physical transmission constraints since it is challenging to analyze the network connectivity in consideration of both the $q$-composite scheme and transmission constraints together. These transmission constraints reflect real-world implementations of sensor networks in which two sensors have to be within a certain distance from each other to communicate. In this paper, we rigorously derive conditions for connectivity in sensor networks employing the $q$-composite scheme under transmission constraints. Furthermore, we extend the analysis to consider the unreliability of wireless links by modeling each link being independently active with some probability. Our results provide useful guidelines for designing securely and reliably connected sensor networks. We also present numerical experiments to confirm the analytical results.

cs.CR↗

arXiv2015

Connectivity in Secure Wireless Sensor Networks under Transmission Constraints

In wireless sensor networks (WSNs), the Eschenauer-Gligor (EG) key pre-distribution scheme is a widely recognized way to secure communications. Although connectivity properties of secure WSNs with the EG scheme have been extensively investigated, few results address physical transmission constraints. These constraints reflect real-world implementations of WSNs in which two sensors have to be within a certain distance from each other to communicate. In this paper, we present zero-one laws for connectivity in WSNs employing the EG scheme under transmission constraints. These laws help specify the critical transmission ranges for connectivity. Our analytical findings are confirmed via numerical experiments. In addition to secure WSNs, our theoretical results are also applied to frequency hopping in wireless networks.

cs.CR↗

arXiv2015

Robustness of power systems under a democratic fiber bundle-like model

We consider a power system with $N$ transmission lines whose initial loads (i.e., power flows) $L_1, \ldots, L_N$ are independent and identically distributed with $P_L(x)$. The capacity $C_i$ defines the maximum flow allowed on line $i$, and is assumed to be given by $C_i=(1+α)L_i$, with $α>0$. We study the robustness of this power system against random attacks (or, failures) that target a $p$-{\em fraction} of the lines, under a democratic fiber bundle-like model. Namely, when a line fails, the load it was carrying is redistributed equally among the remaining lines. Our contributions are as follows: i) we show analytically that the final breakdown of the system always takes place through a first-order transition at the critical attack size $p^{\star}=1-\frac{E[L]}{\max\{P(L>x)(αx + E[L ~|~ L>x])\}}~~~$; ii) we derive conditions on the distribution $P_L(x)$ for which the first order break down of the system occurs abruptly without any preceding diverging rate of failure; iii) we provide a detailed analysis of the robustness of the system under three specific load distributions: Uniform, Pareto, and Weibull, showing that with the minimum load $L_{\textrm{min}}$ and mean load $E[L]$ fixed, Pareto distribution is the worst (in terms of robustness) among the three, whereas Weibull distribution is the best with shape parameter selected relatively large; iv) we provide numerical results that confirm our mean-field analysis; and v) we show that $p^{\star}$ is maximized when the load distribution is a Dirac delta function centered at $E[L]$, i.e., when all lines carry the same load; we also show that optimal $p^{\star}$ equals $\fracα{α+1}$. This last finding is particularly surprising given that heterogeneity is known to lead to high robustness against random failures in many other systems.

physics.soc-ph↗

arXiv2015

A curious gap in one-dimensional geometric random graphs between connectivity and the absence of isolated node

One-dimensional geometric random graphs are constructed by distributing $n$ nodes uniformly and independently on a unit interval and then assigning an undirected edge between any two nodes that have a distance at most $r_n$. These graphs have received much interest and been used in various applications including wireless networks. A threshold of $r_n$ for connectivity is known as $r_n^{*} = \frac{\ln n}{n}$ in the literature. In this paper, we prove that a threshold of $r_n$ for the absence of isolated node is $\frac{\ln n}{2 n}$ (i.e., a half of the threshold $r_n^{*}$). Our result shows there is a curious gap between thresholds of connectivity and the absence of isolated node in one-dimensional geometric random graphs; in particular, when $r_n$ equals $\frac{c\ln n}{ n}$ for a constant $c \in( \frac{1}{2}, 1)$, a one-dimensional geometric random graph has no isolated node but is not connected. This curious gap in one-dimensional geometric random graphs is in sharp contrast to the prevalent phenomenon in many other random graphs such as two-dimensional geometric random graphs, Erdős-Rényi graphs, and random intersection graphs, all of which in the asymptotic sense become connected as soon as there is no isolated node.

physics.soc-ph↗

arXiv2015

Random intersection graphs and their applications in security, wireless communication, and social networks

Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of social networks including common-interest networks, collaboration networks, and actor networks. Simply put, a random intersection graph is constructed by assigning each node a set of items in some random manner and then putting an edge between any two nodes that share a certain number of items. Broadly speaking, our work is about analyzing random intersection graphs, and models generated by composing it with other random graph models including random geometric graphs and Erdős-Rényi graphs. These compositional models are introduced to capture the characteristics of various complex natural or man-made networks more accurately than the existing models in the literature. For random intersection graphs and their compositions with other random graphs, we study properties such as ($k$-)connectivity, ($k$-)robustness, and containment of perfect matchings and Hamilton cycles. Our results are typically given in the form of asymptotically exact probabilities or zero-one laws specifying critical scalings, and provide key insights into the design and analysis of various real-world networks.

cs.DM↗

arXiv2015

Exact Analysis of k-Connectivity in Secure Sensor Networks with Unreliable Links

The Eschenauer--Gligor (EG) random key predistribution scheme has been widely recognized as a typical approach to secure communications in wireless sensor networks (WSNs). However, there is a lack of precise probability analysis on the reliable connectivity of WSNs under the EG scheme. To address this, we rigorously derive the asymptotically exact probability of $k$-connectivity in WSNs employing the EG scheme with unreliable links represented by independent on/off channels, where $k$-connectivity ensures that the network remains connected despite the failure of any $(k-1)$ sensors or links. Our analytical results are confirmed via numerical experiments, and they provide precise guidelines for the design of secure WSNs that exhibit a desired level of reliability against node and link failures.

math.CO↗

arXiv2015

Threshold Functions in Random s-Intersection Graphs

Random $s$-intersection graphs have recently received considerable attention in a wide range of application areas. In such a graph, each vertex is equipped with a set of items in some random manner, and any two vertices establish an undirected edge in between if and only if they have at least $s$ common items. In particular, in a uniform random $s$-intersection graph, each vertex independently selects a fixed number of items uniformly at random from a common item pool, while in a binomial random $s$-intersection graph, each item in some item pool is independently attached to each vertex with the same probability. For binomial/uniform random $s$-intersection graphs, we establish threshold functions for perfect matching containment, Hamilton cycle containment, and $k$-robustness, where $k$-robustness is in the sense of Zhang and Sundaram [IEEE Conf. on Decision & Control '12]. We show that these threshold functions resemble those of classical Erdős-Rényi graphs, where each pair of vertices has an undirected edge independently with the same probability.

physics.soc-ph↗

arXiv2015

k-Connectivity of Random Key Graphs

Random key graphs represent topologies of secure wireless sensor networks that apply the seminal Eschenauer-Gligor random key predistribution scheme to secure communication between sensors. These graphs have received much attention and also been used in diverse application areas beyond secure sensor networks; e.g., cryptanalysis, social networks, and recommender systems. Formally, a random key graph with $n$ nodes is constructed by assigning each node $X_n$ keys selected uniformly at random from a pool of $Y_n$ keys and then putting an undirected edge between any two nodes sharing at least one key. Considerable progress has been made in the literature to analyze connectivity and $k$-connectivity of random key graphs, where $k$-connectivity of a graph ensures connectivity even after the removal of $k$ nodes or $k$ edges. Yet, it still remains an open question for $k$-connectivity in random key graphs under $X_n \geq 2$ and $X_n = o(\sqrt{\ln n})$ (the case of $X_n=1$ is trivial). In this paper, we answer the above problem by providing an exact analysis of $k$-connectivity in random key graphs under $X_n \geq 2$.

physics.soc-ph↗