Related papers: On Dropping Needles and WiFi Link Crossing
Predicting links in complex networks has been one of the essential topics within the realm of data mining and science discovery over the past few years. This problem remains an attempt to identify future, deleted, and redundant links using…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
We consider random walks that start and are absorbed on the leaves of random networks and study the length of such walks. For the networks we investigate, Erdos-Renyi random graphs and Barabasi-Albert scale free networks, these walks are…
An important problem in wireless sensor networks is to find the minimal number of randomly deployed sensors making a network connected with a given probability. In practice sensors are often deployed one by one along a trajectory of a…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in…
We address the question of understanding the effect of the underlying network topology on the spread of a virus and the dissemination of information when users are mobile performing independent random walks on a graph. To this end we…
In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent…
In this paper, we investigate the exact asymptotic behavior of the connectivity probability in the Erdos-Renyi graph G(n,p), under different asymptotic assumptions on the edge probability p=p(n). We propose a novel approach based on the…
We prove for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n has the order of square root of n. Moment or symmetry assumptions are not necessary. In removing…
We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the…
We propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability…
This paper presents results on the typical number of simultaneous point-to-point transmissions above a minimum rate that can be sustained in a network with $n$ transmitter-receiver node pairs when all transmitting nodes can potentially…
The problem of link prediction has attracted considerable recent attention from various domains such as sociology, anthropology, information science, and computer sciences. A link prediction algorithm is proposed based on link similarity…
We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the…
Random walks have been proposed as a simple method of efficiently searching, or disseminating information throughout, communication and sensor networks. In nature, animals (such as ants) tend to follow correlated random walks, i.e., random…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
This work analyzes fractional continuous-time random walks on two-layer multiplexes. A node-centric dynamics is used, in which it is assumed a Poisson distribution of a walker to become active, while a jump to one of its neighbors depends…
We introduce and analyze a new Markov model of the IEEE 802.11 Distributed Coordination Function (DCF) for wireless networks. The new model is derived from a detailed DCF description where transition probabilities are determined by precise…
We study the limit behaviour of a class of random walk models taking values in the $d$-dimensional unit standard simplex, $d\ge 1$, defined as follows. From an interior point $z$, the process chooses one of the $d+1$ vertices of the…