1,419 research outputs found
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
Continuum Line-of-Sight Percolation on Poisson-Voronoi Tessellations
In this work, we study a new model for continuum line-of-sight percolation in
a random environment driven by the Poisson-Voronoi tessellation in the
-dimensional Euclidean space. The edges (one-dimensional facets, or simply
1-facets) of this tessellation are the support of a Cox point process, while
the vertices (zero-dimensional facets or simply 0-facets) are the support of a
Bernoulli point process. Taking the superposition of these two processes,
two points of are linked by an edge if and only if they are sufficiently
close and located on the same edge (1-facet) of the supporting tessellation. We
study the percolation of the random graph arising from this construction and
prove that a 0-1 law, a subcritical phase as well as a supercritical phase
exist under general assumptions. Our proofs are based on a coarse-graining
argument with some notion of stabilization and asymptotic essential
connectedness to investigate continuum percolation for Cox point processes. We
also give numerical estimates of the critical parameters of the model in the
planar case, where our model is intended to represent telecommunications
networks in a random environment with obstructive conditions for signal
propagation.Comment: 30 pages, 4 figures. Accepted for publication in Advances in Applied
Probabilit
Continuum percolation of wireless ad hoc communication networks
Wireless multi-hop ad hoc communication networks represent an
infrastructure-less and self-organized generalization of todays wireless
cellular networks. Connectivity within such a network is an important issue.
Continuum percolation and technology-driven mutations thereof allow to address
this issue in the static limit and to construct a simple distributed protocol,
guaranteeing strong connectivity almost surely and independently of various
typical uncorrelated and correlated random spatial patterns of participating ad
hoc nodes.Comment: 30 pages, to be published in Physica
Connectivity of soft random geometric graphs
Consider a graph on uniform random points in the unit square, each pair
being connected by an edge with probability if the inter-point distance is
at most . We show that as the probability of full connectivity
is governed by that of having no isolated vertices, itself governed by a
Poisson approximation for the number of isolated vertices, uniformly over all
choices of . We determine the asymptotic probability of connectivity for
all subject to , some . We
generalize the first result to higher dimensions and to a larger class of
connection probability functions.Comment: Published at http://dx.doi.org/10.1214/15-AAP1110 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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.Comment: Full version of a paper published in Annual Allerton Conference on
Communication, Control, and Computing (Allerton) 201
On the freezing of variables in random constraint satisfaction problems
The set of solutions of random constraint satisfaction problems (zero energy
groundstates of mean-field diluted spin glasses) undergoes several structural
phase transitions as the amount of constraints is increased. This set first
breaks down into a large number of well separated clusters. At the freezing
transition, which is in general distinct from the clustering one, some
variables (spins) take the same value in all solutions of a given cluster. In
this paper we study the critical behavior around the freezing transition, which
appears in the unfrozen phase as the divergence of the sizes of the
rearrangements induced in response to the modification of a variable. The
formalism is developed on generic constraint satisfaction problems and applied
in particular to the random satisfiability of boolean formulas and to the
coloring of random graphs. The computation is first performed in random tree
ensembles, for which we underline a connection with percolation models and with
the reconstruction problem of information theory. The validity of these results
for the original random ensembles is then discussed in the framework of the
cavity method.Comment: 32 pages, 7 figure
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