The Threshold Behaviour of the Fixed Radius Random Graph Model and Applications to the Key Management Problem of Sensor Networks

Liagkou, Vasiliki; Makri, Effie; Spirakis, Paul G.; Stamatiou, Yannis C.

doi:10.1007/11963271_12

Cited by 7 publications

(7 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For instance, if graph nodes model system components (e.g. sensors) that move about in Euclidean space and adjacency between pairs of them is decided according the their transmission range, the fixed radius model is a good choice for modeling the network (see, e.g., (Liagkou et al, 2006)). If, however, one is interested in patterns arising in the Internet graph, the preferential random graph model is best.…”

Section: A Generic Trust Model Based On Threshold Laws For Mathematicmentioning

confidence: 99%

“…In (Liagkou et al, 2006) we proved that fixed radius random graph model has a threshold behavior in order to introduce a key distribution scheme. Here we use the following Lemma and Theorems in order to demonstrate that a number of global system properties related to trust can be described in the first order language of graphs and that they hold with probability 1 for certain ranges of the fixed radius random graph model.…”

Section: Threshold Behavior Of the Fixed Radius Random Graph Modelmentioning

confidence: 99%

See 1 more Smart Citation

Trust in global computing systems as a limit property emerging from short range random interactions

Liagkou

Makri

Spirakis

et al. 2007

The Second International Conference on Availability, Reliability and Security (ARES'07)

Self Cite

View full text Add to dashboard Cite

Trust in global computing systems as a limit property emerging from short range random interactions 125 Effie Makri University of the Aegean, Department of Mathematics Greece AbstractToday we are witnessing a major reconsideration of the computing paradigm, as evidenced by the abundance and increasing frequency of use of novel terms such as ambient intelligence, ubiquitous computing, disappearing computer, grid computer, global computing and mobile ad-hoc networks. Systems that can be described with such terms are of a dynamic, with no clear physical boundary, nature and it seems that it is impossible (or, at least, difficult) to define sharply a number of important properties holding with certainty and throughout the whole lifetime of the system. In this chapter we propose a new paradigm for the concept of trust that can be applicable to describing trust related properties in evolving, "boundary-transcending", computing systems. This paradigm is founded on the interaction between formal logic and threshold phenomena, i.e. properties of large combinatorial structures that can be proved to emerge with certainty, as the system evolves. We define a number of notions of trust within these frameworks and pinpoint their inherent weakness in providing clear and measurable trust properties. We then argue that trust in dynamic, global computing systems must, necessarily, incorporate, to some degree, some non-formalizable elements, such as common sense and intuition in order to overcome formalism's weaknesses and result in a pragmatic notion of trust applicable to today's new computing paradigms.

show abstract

Section: A Generic Trust Model Based On Threshold Laws For Mathematicmentioning

confidence: 99%

Section: Threshold Behavior Of the Fixed Radius Random Graph Modelmentioning

confidence: 99%

Trust in global computing systems as a limit property emerging from short range random interactions

Liagkou

Makri

Spirakis

et al. 2007

The Second International Conference on Availability, Reliability and Security (ARES'07)

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, some security aspects that can be mathematically described using a special logic described in Section 3 can still be studied theoretically under the proposed model (see [3] on the key management issue for sensor networks).…”

Section: The Modelmentioning

confidence: 99%

“…The connection of the distribution function D 2 (x) for the distance between random points on the circle of radius R and the probability that the extension statement is given by the following lemma (see [3]):…”

Section: Random Points In D-dimensional Spheres and Emergent Propertiesmentioning

confidence: 99%

The digital territory: a mathematical model of the concept and its properties

Kameas

Stamatiou²

2006

2nd IET International Conference on Intelligent Environments (IE 06)

View full text Add to dashboard Cite

In this paper we attempt to define a mathematical model for the formal study of the concept of Digital Territories (DT) and its properties. We describe a simple DT model and employ the first order language of graphs and random graph properties in order to define and study properties of DTs that emerge as soon as the entities (within the DT) population reaches certain threshold points. Our aim is to show that the DT concept can be formalized and studied using mathematical tools that are within reach of any researcher in the DT domain in order to describe and study properties of interest.

show abstract

“…Ç ó÷åôéêÞ åñåõíçôéêÞ äïõëåéÜ áíáöÝñåôáé óôá áíôßóôïé÷á êåöÜëáéá ôïõ äåýôåñïõ ìÝñïõò ôùí ìïíôÝëùí êáé ôùí ðñùôïêüëëùí. ÔÝëïò ç ðáñïýóá äéäáêôïñéêÞ äéáôñéâÞ ðåñéëáìâÜíåé åñåõíçôéêÜ áðïôåëÝóìáôá, ôá ïðïßá äçìïóéåýôçêáí óôéò åñãáóßåò [55], [21], [22], [58], [57], [56] êáé [23].…”

Section: åéóáãùãþunclassified

Ασφαλή Και Έμπιστα Πρωτόκολλα Επικοινωνιών Με Χρήση Κρυπτογραφίας Και Κρυπτανάλυσης

Λιάγκου¹

View full text Add to dashboard Cite

The Threshold Behaviour of the Fixed Radius Random Graph Model and Applications to the Key Management Problem of Sensor Networks

Cited by 7 publications

References 3 publications

Trust in global computing systems as a limit property emerging from short range random interactions

Trust in global computing systems as a limit property emerging from short range random interactions

The digital territory: a mathematical model of the concept and its properties

Ασφαλή Και Έμπιστα Πρωτόκολλα Επικοινωνιών Με Χρήση Κρυπτογραφίας Και Κρυπτανάλυσης

Contact Info

Product

Resources

About