Geometric Graphs with Randomly Deleted Edges - Connectivity and Routing Protocols

Krzywdziński, Krzysztof; Rybarczyk, Katarzyna

doi:10.1007/978-3-642-22993-0_49

Cited by 25 publications

(55 citation statements)

References 21 publications

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“…This was done under the additional conditions that P n = (n) (required only for the one-law) and that lim n→∞ p n ln n exists (required only for the zero-law). However, Theorem 1 given here establishes (by setting k = 1) that, if p e = ln n + α n n (23) then G on is a.a.s. connected if lim n→∞ α n = ∞, and it is a.a.s.…”

Section: Discussion and Comparison With Related Resultsmentioning

confidence: 93%

<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Connectivity in Random Key Graphs With Unreliable Links

Zhao

Yağan

Gligor

2015

IEEE Trans. Inform. Theory

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Random key graphs form a class of random intersection graphs that 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 attention 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 graph links is captured by independent Bernoulli random variables, rendering them to be on or off independently from each other. The resulting model is an intersection of a random key graph and an Erdős-Rényi 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: 1) the minimum node degree in the graph is at least k and 2) the graph is k-connected, both with high probability as the number of nodes becomes large. The results are given in the form of zero-one laws with critical thresholds identified and shown to coincide for both graph properties. These findings improve the previous results by Rybarczyk on k-connectivity of random key graphs (with reliable links), as well as the zero-one laws by Yagan on one-connectivity of random key graphs with unreliable links.

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Section: Discussion and Comparison With Related Resultsmentioning

confidence: 93%

<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Connectivity in Random Key Graphs With Unreliable Links

Zhao

Yağan

Gligor

2015

IEEE Trans. Inform. Theory

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“…In fact, in a recent paper [28] it was pointed out that K. Krzywdziński and K. Rybarczyk [17] had proved that if…”

Section: Conclusion: the Wider Implications Of Our Resultsmentioning

confidence: 99%

Optimal radius for connectivity in duty-cycled wireless sensor networks

Bagchi

Pinotti

Galhotra

et al. 2013

Proceedings of the 16th ACM International Conference on Modeling, Analysis &Amp; Simulation of Wireless and Mobile Systems

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We investigate the condition on transmission radius needed to achieve connectivity in duty-cycled wireless sensor networks (briefly, DC-WSN). First, we settle a conjecture of and prove that the connectivity condition on Random Geometric Graphs (RGG), given by Gupta and Kumar (1989), can be used to derive a weak sufficient condition to achieve connectivity in DC-WSN. To find a stronger result, we define a new vertex-based random connection model which is of independent interest. Following a proof technique of Penrose (1991) we prove that when the density of the nodes approaches infinity then a finite component of size greater than 1 exists with probability 0 in this model. We use this result to obtain an optimal condition on node transmission radius which is both necessary and sufficient to achieve connectivity and is hence optimal. The optimality of such a radius is also tested via simulation for two specific duty-cycle schemes, called the contiguous and the random selection duty-cycle scheme. Finally, we design a minimum-radius duty-cycling scheme that achieves connectivity with a transmission radius arbitrarily close to the one required in Random Geometric Graphs. The overhead in this case is that we have to spend some time computing the schedule.

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“…Such network area A is either a torus T or a square S, each of unit area, depending on whether the boundary effect exists or not [98]. The boundary effect arises whenever part of the transmission area of a node may fall outside the network area A. T does not have the boundary effect, whereas S has the boundary effect [99][100][101].…”

Section: Disk Modelmentioning

confidence: 99%

Wireless Sensor Network Based Smart Grid Communications: Cyber Attacks, Intrusion Detection System and Topology Control

et al. 2017

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Abstract:The existing power grid is going through a massive transformation. Smart grid technology is a radical approach for improvisation in prevailing power grid. Integration of electrical and communication infrastructure is inevitable for the deployment of Smart grid network. Smart grid technology is characterized by full duplex communication, automatic metering infrastructure, renewable energy integration, distribution automation and complete monitoring and control of entire power grid. Wireless sensor networks (WSNs) are small micro electrical mechanical systems that are deployed to collect and communicate the data from surroundings. WSNs can be used for monitoring and control of smart grid assets. Security of wireless sensor based communication network is a major concern for researchers and developers. The limited processing capabilities of wireless sensor networks make them more vulnerable to cyber-attacks. The countermeasures against cyber-attacks must be less complex with an ability to offer confidentiality, data readiness and integrity. The address oriented design and development approach for usual communication network requires a paradigm shift to design data oriented WSN architecture. WSN security is an inevitable part of smart grid cyber security. This paper is expected to serve as a comprehensive assessment and analysis of communication standards, cyber security issues and solutions for WSN based smart grid infrastructure.

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Geometric Graphs with Randomly Deleted Edges - Connectivity and Routing Protocols

Cited by 25 publications

References 21 publications

<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Connectivity in Random Key Graphs With Unreliable Links

<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Connectivity in Random Key Graphs With Unreliable Links

Optimal radius for connectivity in duty-cycled wireless sensor networks

Wireless Sensor Network Based Smart Grid Communications: Cyber Attacks, Intrusion Detection System and Topology Control

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