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Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many…

Disordered Systems and Neural Networks · Physics 2018-09-27 Carl P. Dettmann

We consider the following interference model for wireless sensor and ad hoc networks: the receiver interference of a node is the number of transmission ranges it lies in. We model transmission ranges as disks. For this case we show that…

Networking and Internet Architecture · Computer Science 2011-10-11 Kevin Buchin

Three closely-related polynomial-based group key pre-distribution schemes have recently been proposed, aimed specifically at wireless sensor networks. The schemes enable any subset of a predefined set of sensor nodes to establish a shared…

Cryptography and Security · Computer Science 2026-03-20 Chris J Mitchell

Many applications of wireless sensor networks (WSNs) require deploying sensors in hostile environments, where an adversary may eavesdrop communications. To secure communications in WSNs, the q-composite key predistribution scheme has been…

Information Theory · Computer Science 2019-11-05 Jun Zhao

Generally traffic and the sensor network security have many challenges in the transmission of data in the network. The existing schemes consider homogeneous sensor networks which have poor performance and scalability. Due to many-to-one…

Networking and Internet Architecture · Computer Science 2012-02-10 P. Karunakaran , Dr. C. Venkatesh

Due to resource constraints of the sensor nodes, traditional public key cryptographic techniques are not feasible in most sensor network architectures. Several symmetric key distribution mechanisms are proposed for establishing pairwise…

Cryptography and Security · Computer Science 2011-03-24 Ashok Kumar Das

The ability to exchange secret information is critical to many commercial, governmental, and military networks. The intrinsically secure communications graph (iS-graph) is a random graph which describes the connections that can be securely…

Information Theory · Computer Science 2016-11-17 Pedro C. Pinto , Joao Barros , Moe Z. Win

The secrecy graph is a random geometric graph which is intended to model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the…

Probability · Mathematics 2012-08-15 Amites Sarkar , Martin Haenggi

We propose and analyze a graph model to study the connectivity of interdependent networks. Two interdependent networks of arbitrary topologies are modeled as two graphs, where every node in one graph is supported by supply nodes in the…

Discrete Mathematics · Computer Science 2018-09-10 Jianan Zhang , Eytan Modiano

This paper, based on $k$-NN graph, presents symmetric $(k,j)$-NN graph $(1 \leq j < k)$, a brand new topology which could be adopted by a series of network-based structures. We show that the $k$ nearest neighbors of a node exert disparate…

Networking and Internet Architecture · Computer Science 2014-10-30 Jie Ding , Min-Yi Wang , Qiao Wang , Xin-Shan Zhu

We study the heterogeneous wireless sensor networks (WSNs) and propose the necessary condition of the optimal sensor deployment. Similar to that in homogeneous WSNs, the necessary condition implies that every sensor node location should…

Networking and Internet Architecture · Computer Science 2016-03-29 Jun Guo , Hamid Jafarkhani

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…

Combinatorics · Mathematics 2015-02-09 Jun Zhao , Osman Yağan , Virgil Gligor

We study the number of isolated nodes in a soft random geometric graph whose vertices constitute a Poisson process on the torus of length L (the line segment [0,L] with periodic boundary conditions), and where an edge is present between two…

Probability · Mathematics 2022-10-21 Michael Wilsher , Carl Dettmann , Ayalvadi Ganesh

A \emph{uniform random intersection graph} $G(n,m,k)$ is a random graph constructed as follows. Label each of $n$ nodes by a randomly chosen set of $k$ distinct colours taken from some finite set of possible colours of size $m$. Nodes are…

Combinatorics · Mathematics 2008-12-03 Simon R. Blackburn , Stefanie Gerke

The security of wireless sensor networks is an active topic of research where both symmetric and asymmetric key cryptography issues have been studied. Due to their computational feasibility on typical sensor nodes, symmetric key algorithms…

Cryptography and Security · Computer Science 2008-03-10 Abedelaziz Mohaisen , DaeHun Nyang , KyungHee Lee

We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…

Statistical Mechanics · Physics 2017-09-13 Reimer Kuehn , Tim Rogers

Wireless sensor networks (WSNs) are considered as a major technology enabling the Internet of Things (IoT) paradigm. The recent emerging Graph Signal Processing field can also contribute to enabling the IoT by providing key tools, such as…

Signal Processing · Electrical Eng. & Systems 2020-07-16 Leila Ben Saad , Baltasar Beferull-Lozano

In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on…

Probability · Mathematics 2021-01-04 Michael Wilsher , Carl P. Dettmann , Ayalvadi Ganesh

In the present paper, we derive an upper bound of the average network breakdown probability of packet networks with unreliable relay nodes. We here assume that relay nodes get independently broken with a given node breakdown probability. A…

Information Theory · Computer Science 2017-01-25 Takayuki Nozaki , Takafumi Nakano , Tadashi Wadayama

Despite much research on probabilistic key predistribution schemes for wireless sensor networks over the past decade, few formal analyses exist that define schemes' resilience to node-capture attacks precisely and under realistic…

Cryptography and Security · Computer Science 2019-11-05 Jun Zhao