arXiv subjects

Emilio Leonardi

Publications and source records attributed to Emilio Leonardi.

At least 37 records · Page 2Linked to original sources

arXiv2020

A large deviation approach to super-critical bootstrap percolation on the random graph $G_{n,p}$

We consider the Erdös--Rényi random graph $G_{n,p}$ and we analyze the simple irreversible epidemic process on the graph, known in the literature as bootstrap percolation. We give a quantitative version of some results by Janson et al. (2012), providing a fine asymptotic analysis of the final size $A_n^*$ of active nodes, under a suitable super-critical regime. More specifically, we establish large deviation principles for the sequence of random variables $\{\frac{n- A_n^*}{f(n)}\}_{n\geq 1}$ with explicit rate functions and allowing the scaling function $f$ to vary in the widest possible range.

math.PR↗

arXiv2019

Almost Sure Central Limit Theorems in Stochastic Geometry

We prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals emerging in stochastic geometry. As a consequence, we provide almost sure central limit theorems for $(i)$ the total edge length of the $k$-nearest neighbors random graph, $(ii)$ the clique count in random geometric graphs, $(iii)$ the volume of the set approximation via the Poisson-Voronoi tessellation.

math.PR↗

arXiv2019

Opinion Dynamics on Correlated Subjects in Social Networks

Understanding the evolution of collective beliefs is of critical importance to get insights on the political trends as well as on social tastes and opinions. In particular, it is pivotal to develop analytical models that can predict the beliefs dynamics and capture the interdependence of opinions on different subjects. In this paper we tackle this issue also accounting for the individual endogenous process of opinion evolution, as well as repulsive interactions between individuals' opinions that may arise in the presence of an adversarial attitude of the individuals. Using a mean field approach, we characterize the time evolution of opinions of a large population of individuals through a multidimensional Fokker-Planck equation, and we identify the conditions under which stability holds. Finally, we derive the steady-state opinion distribution as a function of the individuals' personality and of the existing social interactions. Our numerical results show interesting dynamics in the collective beliefs of different social communities, and they highlight the effect of correlated subjects as well as of individuals with an adversarial attitude.

cs.SI↗

arXiv2019

Cache Subsidies for an Optimal Memory for Bandwidth Tradeoff in the Access Network

While the cost of the access network could be considerably reduced by the use of caching, this is not currently happening because content providers (CPs), who alone have the detailed demand data required for optimal content placement, have no natural incentive to use them to minimize access network operator (ANO) expenditure. We argue that ANOs should therefore provide such an incentive in the form of direct subsidies paid to the CPs in proportion to the realized savings. We apply coalition game theory to design the required subsidy framework and propose a distributed algorithm, based on Lagrangian decomposition, allowing ANOs and CPs to collectively realize the optimal memory for bandwidth tradeoff. The considered access network is a cache hierarchy with per-CP central office caches, accessed by all ANOs, at the apex, and per-ANO dedicated bandwidth and storage resources at the lower levels, including wireless base stations, that must be shared by multiple CPs.

cs.NI↗

arXiv2019

Impact of Traffic Characteristics on Request Aggregation in an NDN Router

The paper revisits the performance evaluation of caching in a Named Data Networking (NDN) router where the content store (CS) is supplemented by a pending interest table (PIT). The PIT aggregates requests for a given content that arrive within the download delay and thus brings an additional reduction in upstream bandwidth usage beyond that due to CS hits. We extend prior work on caching with non-zero download delay (non-ZDD) by proposing a novel mathematical framework that is more easily applicable to general traffic models and by considering alternative cache insertion policies. Specifically we evaluate the use of an LRU filter to improve CS hit rate performance in this non-ZDD context. We also consider the impact of time locality in demand due to finite content lifetimes. The models are used to quantify the impact of the PIT on upstream bandwidth reduction, demonstrating notably that this is significant only for relatively small content catalogues or high average request rate per content. We further explore how the effectiveness of the filter with finite content lifetimes depends on catalogue size and traffic intensity.

cs.NI↗

arXiv2018

Implicit Coordination of Caches in Small Cell Networks under Unknown Popularity Profiles

We focus on a dense cellular network, in which a limited-size cache is available at every Base Station (BS). In order to optimize the overall performance of the system in such scenario, where a significant fraction of the users is covered by several BSs, a tight coordination among nearby caches is needed. To this end, this pape introduces a class of simple and fully distributed caching policies, which require neither direct communication among BSs, nor a priori knowledge of content popularity. Furthermore, we propose a novel approximate analytical methodology to assess the performance of interacting caches under such policies. Our approach builds upon the well known characteristic time approximation and provides predictions that are surprisingly accurate (hardly distinguishable from the simulations) in most of the scenarios. Both synthetic and trace-driven results show that the our caching policies achieve excellent performance (in some cases provably optimal). They outperform state-of-the-art dynamic policies for interacting caches, and, in some cases, also the greedy content placement, which is known to be the best performing polynomial algorithm under static and perfectly-known content popularity profiles.

cs.NI↗

arXiv2017

Selecting the top-quality item through crowd scoring

We investigate crowdsourcing algorithms for finding the top-quality item within a large collection of objects with unknown intrinsic quality values. This is an important problem with many relevant applications, for example in networked recommendation systems. The core of the algorithms is that objects are distributed to crowd workers, who return a noisy and biased evaluation. All received evaluations are then combined, to identify the top-quality object. We first present a simple probabilistic model for the system under investigation. Then, we devise and study a class of efficient adaptive algorithms to assign in an effective way objects to workers. We compare the performance of several algorithms, which correspond to different choices of the design parameters/metrics. In the simulations we show that some of the algorithms achieve near optimal performance for a suitable setting of the system parameters.

cs.HC↗

arXiv2017

Belief Dynamics in Social Networks: A Fluid-Based Analysis

The advent and proliferation of social media have led to the development of mathematical models describing the evolution of beliefs/opinions in an ecosystem composed of socially interacting users. The goal is to gain insights into collective dominant social beliefs and into the impact of different components of the system, such as users' interactions, while being able to predict users' opinions. Following this thread, in this paper we consider a fairly general dynamical model of social interactions, which captures all the main features exhibited by a social system. For such model, by embracing a mean-field approach, we derive a diffusion differential equation that represents asymptotic belief dynamics, as the number of users grows large. We then analyze the steady-state behavior as well as the time dependent (transient) behavior of the system. In particular, for the steady-state distribution, we obtain simple closed-form expressions for a relevant class of systems, while we propose efficient semi-analytical techniques in the most general cases. At last, we develop an efficient semi-analytical method to analyze the dynamics of the users' belief over time, which can be applied to a remarkably large class of systems.

cs.SI↗

arXiv2016

Modeling LRU caches with Shot Noise request processes

In this paper we analyze Least Recently Used (LRU) caches operating under the Shot Noise requests Model (SNM). The SNM was recently proposed to better capture the main characteristics of today Video on Demand (VoD) traffic. We investigate the validity of Che's approximation through an asymptotic analysis of the cache eviction time. In particular, we provide a large deviation principle, a law of large numbers and a central limit theorem for the cache eviction time, as the cache size grows large. Finally, we derive upper and lower bounds for the "hit" probability in tandem networks of caches under Che's approximation.

cs.PF↗

arXiv2016

Generalized threshold-based epidemics in random graphs: the power of extreme values

Bootstrap percolation is a well-known activation process in a graph, in which a node becomes active when it has at least $r$ active neighbors. Such process, originally studied on regular structures, has been recently investigated also in the context of random graphs, where it can serve as a simple model for a wide variety of cascades, such as the spreading of ideas, trends, viral contents, etc. over large social networks. In particular, it has been shown that in $G(n,p)$ the final active set can exhibit a phase transition for a sub-linear number of seeds. In this paper, we propose a unique framework to study similar sub-linear phase transitions for a much broader class of graph models and epidemic processes. Specifically, we consider i) a generalized version of bootstrap percolation in $G(n,p)$ with random activation thresholds and random node-to-node influences; ii) different random graph models, including graphs with given degree sequence and graphs with community structure (block model). The common thread of our work is to show the surprising sensitivity of the critical seed set size to extreme values of distributions, which makes some systems dramatically vulnerable to large-scale outbreaks. We validate our results running simulation on both synthetic and real graphs.

cs.SI↗

arXiv2016

A unified approach to the performance analysis of caching systems

We propose a unified methodology to analyse the performance of caches (both isolated and interconnected), by extending and generalizing a decoupling technique originally known as Che's approximation, which provides very accurate results at low computational cost. We consider several caching policies, taking into account the effects of temporal locality. In the case of interconnected caches, our approach allows us to do better than the Poisson approximation commonly adopted in prior work. Our results, validated against simulations and trace-driven experiments, provide interesting insights into the performance of caching systems.

cs.NI↗

arXiv2015

Unravelling the Impact of Temporal and Geographical Locality in Content Caching Systems

To assess the performance of caching systems, the definition of a proper process describing the content requests generated by users is required. Starting from the analysis of traces of YouTube video requests collected inside operational networks, we identify the characteristics of real traffic that need to be represented and those that instead can be safely neglected. Based on our observations, we introduce a simple, parsimonious traffic model, named Shot Noise Model (SNM), that allows us to capture temporal and geographical locality of content popularity. The SNM is sufficiently simple to be effectively employed in both analytical and scalable simulative studies of caching systems. We demonstrate this by analytically characterizing the performance of the LRU caching policy under the SNM, for both a single cache and a network of caches. With respect to the standard Independent Reference Model (IRM), some paradigmatic shifts, concerning the impact of various traffic characteristics on cache performance, clearly emerge from our results.

cs.NI↗

arXiv2014

Efficient analysis of caching strategies under dynamic content popularity

In this paper we develop a novel technique to analyze both isolated and interconnected caches operating under different caching strategies and realistic traffic conditions. The main strength of our approach is the ability to consider dynamic contents which are constantly added into the system catalogue, and whose popularity evolves over time according to desired profiles. We do so while preserving the simplicity and computational efficiency of models developed under stationary popularity conditions, which are needed to analyze several caching strategies. Our main achievement is to show that the impact of content popularity dynamics on cache performance can be effectively captured into an analytical model based on a fixed content catalogue (i.e., a catalogue whose size and objects' popularity do not change over time).

cs.PF↗

arXiv2014

De-anonymizing scale-free social networks by percolation graph matching

We address the problem of social network de-anonymization when relationships between people are described by scale-free graphs. In particular, we propose a rigorous, asymptotic mathematical analysis of the network de-anonymization problem while capturing the impact of power-law node degree distribution, which is a fundamental and quite ubiquitous feature of many complex systems such as social networks. By applying bootstrap percolation and a novel graph slicing technique, we prove that large inhomogeneities in the node degree lead to a dramatic reduction of the initial set of nodes that must be known a priori (the seeds) in order to successfully identify all other users. We characterize the size of this set when seeds are selected using different criteria, and we show that their number can be as small as $n^ε$, for any small ${ε>0}$. Our results are validated through simulation experiments on a real social network graph.

cs.SI↗

arXiv2014

The Importance of Being Earnest in Crowdsourcing Systems

This paper presents the first systematic investigation of the potential performance gains for crowdsourcing systems, deriving from available information at the requester about individual worker earnestness (reputation). In particular, we first formalize the optimal task assignment problem when workers' reputation estimates are available, as the maximization of a monotone (submodular) function subject to Matroid constraints. Then, being the optimal problem NP-hard, we propose a simple but efficient greedy heuristic task allocation algorithm. We also propose a simple ``maximum a-posteriori`` decision rule. Finally, we test and compare different solutions, showing that system performance can greatly benefit from information about workers' reputation. Our main findings are that: i) even largely inaccurate estimates of workers' reputation can be effectively exploited in the task assignment to greatly improve system performance; ii) the performance of the maximum a-posteriori decision rule quickly degrades as worker reputation estimates become inaccurate; iii) when workers' reputation estimates are significantly inaccurate, the best performance can be obtained by combining our proposed task assignment algorithm with the LRA decision rule introduced in the literature.

cs.HC↗

arXiv2014

Throughput Optimal Scheduling Policies in Networks of Interacting Queues

This report considers a fairly general model of constrained queuing networks that allows us to represent both MMBP (Markov Modulated Bernoulli Processes) arrivals and time-varying service constraints. We derive a set of sufficient conditions for throughput optimality of scheduling policies that encompass and generalize all the previously obtained results in the field. This leads to the definition of new classes of (non diagonal) throughput optimal scheduling policies. We prove the stability of queues by extending the traditional Lyapunov drift criteria methodology.

cs.PF↗

arXiv2014

Large deviations of the interference in the Ginibre network model

Under different assumptions on the distribution of the fading random variables, we derive large deviation estimates for the tail of the interference in a wireless network model whose nodes are placed, over a bounded region of the plane, according to the $β$-Ginibre process, $0<β\leq 1$. The family of $β$-Ginibre processes is formed by determinantal point processes, with different degree of repulsiveness, which converge in law to a homogeneous Poisson process, as $β\to 0$. In this sense the Poisson network model may be considered as the limiting uncorrelated case of the $β$-Ginibre network model. Our results indicate the existence of two different regimes. When the fading random variables are bounded or Weibull superexponential, large values of the interference are typically originated by the sum of several equivalent interfering contributions due to nodes in the vicinity of the receiver. In this case, the tail of the interference has, on the log-scale, the same asymptotic behavior for any value of $0<β\le 1$, but it differs (again on a log-scale) from the asymptotic behavior of the tail of the interference in the Poisson network model. When the fading random variables are exponential or subexponential, instead, large values of the interference are typically originated by a single dominating interferer node and, on the log-scale, the asymptotic behavior of the tail of the interference is essentially insensitive to the distribution of the nodes. As a consequence, on the log-scale, the asymptotic behavior of the tail of the interference in any $β$-Ginibre network model, $0<β\le 1$, is the same as in the Poisson network model.

cs.IT↗

arXiv2013

Temporal Locality in Today's Content Caching: Why it Matters and How to Model it

The dimensioning of caching systems represents a difficult task in the design of infrastructures for content distribution in the current Internet. This paper addresses the problem of defining a realistic arrival process for the content requests generated by users, due its critical importance for both analytical and simulative evaluations of the performance of caching systems. First, with the aid of YouTube traces collected inside operational residential networks, we identify the characteristics of real traffic that need to be considered or can be safely neglected in order to accurately predict the performance of a cache. Second, we propose a new parsimonious traffic model, named the Shot Noise Model (SNM), that enables users to natively capture the dynamics of content popularity, whilst still being sufficiently simple to be employed effectively for both analytical and scalable simulative studies of caching systems. Finally, our results show that the SNM presents a much better solution to account for the temporal locality observed in real traffic compared to existing approaches.

cs.NI↗