New results on a generalized coupon collector problem using Markov chains

We study in this paper a generalized coupon collector problem, which consists in determining the distribution and the moments of the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an arbitrary probability distribution. We suppose that a special coupon called the null coupon can be drawn but never belongs to any collection. In this context, we obtain expressions of the distribution and the moments of this time. We also prove that the almost-uniform distribution, for which all the non-null coupons have the same drawing probability, is the distribution which minimizes the expected time to get a fixed subset of distinct coupons. This optimization result is extended to the complementary distribution of that time when the full collection is considered, proving by the way this well-known conjecture. Finally, we propose a new conjecture which expresses the fact that the almost-uniform distribution should minimize the complementary distribution of the time needed to get any fixed number of distinct coupons.Comment: 14 page

D.4.1 – Application scenarii and Design of infrastructure

This report has been written by all members of the consortiumSocioPlug is a research project, funded by French National Agency for Research, which aims to investigate on Social Cloud over Plug Networks, Enabling Symmetric Access to Data and Preserving Privacy. In this project, we will perform both theoretical and practical evaluation of the solutions proposed in the all work packages. Task 4 (Infrastructure and Experimentation) will be structured around use-cases where partners developed previous expertise such as distributed collaborative systems, social web and Smart Building. These well known distributed systems will be revisited to fit federation of plug constraints using results of other tasks. In this deliverable, we present some details of the infrastructure of the federation of plug computers, that will be developed in this project. We plan to provide a demonstrator and deploy on it some application according to the use-cases presented in this deliverable

Optimization results for a generalized coupon collector problem

We study in this paper a generalized coupon collector problem, which consists in analyzing the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an arbitrary probability distribution. We suppose that a special coupon called the null coupon can be drawn but never belongs to any collection. In this context, we prove that the almost uniform distribution, for which all the non-null coupons have the same drawing probability, is the distribution which stochastically minimizes the time needed to collect a fixed number of distinct coupons. Moreover, we show that in a given closed subset of probability distributions, the distribution with all its entries, but one, equal to the smallest possible value is the one, which stochastically maximizes the time needed to collect a fixed number of distinct coupons. An computer science application shows the utility of these results.Comment: arXiv admin note: text overlap with arXiv:1402.524

GCP: Gossip-based Code Propagation for Large-scale Mobile Wireless Sensor Networks

Wireless sensor networks (WSN) have recently received an increasing interest. They are now expected to be deployed for long periods of time, thus requiring software updates. Updating the software code automatically on a huge number of sensors is a tremendous task, as ''by hand'' updates can obviously not be considered, especially when all participating sensors are embedded on mobile entities. In this paper, we investigate an approach to automatically update software in mobile sensor-based application when no localization mechanism is available. We leverage the peer-to-peer cooperation paradigm to achieve a good trade-off between reliability and scalability of code propagation. More specifically, we present the design and evaluation of GCP ({\emph Gossip-based Code Propagation}), a distributed software update algorithm for mobile wireless sensor networks. GCP relies on two different mechanisms (piggy-backing and forwarding control) to improve significantly the load balance without sacrificing on the propagation speed. We compare GCP against traditional dissemination approaches. Simulation results based on both synthetic and realistic workloads show that GCP achieves a good convergence speed while balancing the load evenly between sensors

Nothing can compare with a population, besides agents

15 pagesLeveraging the resemblances between two areas explored so far independently enables to provide a theoretical framework for dis- tributed systems where global behaviors emerge from a set of local in- teractions. The contribution of this paper arise from the observation that population protocols and multi-agent systems (MAS) bear many resemblances. Particularly, some subclasses of MAS seem to fit the same computational power than population protocols. Population protocols provide theoretical foundations for mobile tiny device networks. On the other hand, from long-standing research study in distributed artificial in- telligence, MAS forms an interesting model for society and owns a broad spectrum of application field, from simple reactive system to social sci- ences. Linking the both model should offers several extremely interesting outcomes

AnKLe: détection automatique d'attaques par divergence d'information

4 pagesInternational audienceDans cet article, nous considérons le contexte de très grands systèmes distribués, au sein desquels chaque noeud doit pouvoir rapidement analyser une grande quantité d'information, lui arrivant sous la forme d'un flux. Ce dernier ayant pu être modifié par un adversaire, un problème fondamental consiste en la détection et la quantification d'actions malveillantes effectuées sur ce flux. Dans ce but, nous proposons AnKLe (pour Attack-tolerant eNhanced Kullback-Leibler divergence Estimator), un algorithme local permettant d'estimer la divergence de Kullback-Leibler entre un flux observé et le flux espéré. AnKLe combine des techniques d'échantillonnage et des méthodes de théorie de l'information. Il est efficace à la fois en complexité en terme d'espace et en temps, et ne nécessite qu'une passe unique sur le flux. Les résultats expérimentaux montre que l'estimateur fourni par AnKLe est pertinent pour plusieurs types d'attaques, pour lesquels les autres méthodes existantes sont significativement moins performantes

Uniform Node Sampling Service Robust against Collusions of Malicious Nodes

International audienceWe consider the problem of achieving uniform node sampling in large scale systems in presence of a strong adversary. We first propose an omniscient strategy that processes on the fly an unbounded and arbitrarily biased input stream made of node identifiers exchanged within the system, and outputs a stream that preserves Uniformity and Freshness properties. We show through Markov chains analysis that both properties hold despite any arbitrary bias introduced by the adversary. We then propose a knowledge-free strategy and show through extensive simulations that this strategy accurately approximates the omniscient one. We also evaluate its resilience against a strong adversary by studying two representative attacks (flooding and targeted attacks). We quantify the minimum number of identifiers that the adversary must insert in the input stream to prevent uniformity. To our knowledge, such an analysis has never been proposed before

AnKLe: Detecting Attacks in Large Scale Systems via Information Divergence

In this paper, we consider the setting of large scale distributed systems, in which each node needs to quickly process a huge amount of data received in the form of a stream that may have been tampered with by an adversary. In this situation, a fundamental problem is how to detect and quantify the amount of work performed by the adversary. To address this issue, we propose AnKLe (for Attack-tolerant eNhanced Kullback-Leibler divergence Estimator), a novel algorithm for estimating the KL divergence of an observed stream compared to the expected one. AnKLe combines sampling techniques and information-theoretic methods. It is very efficient, both in terms of space and time complexities, and requires only a single pass over the data stream. Experimental results show that the estimation provided by AnKLe remains accurate even for different adversarial settings for which the quality of other methods dramatically decreases

On the Power of the Adversary to Solve the Node Sampling Problem

International audienceWe study the problem of achieving uniform and fresh peer sampling in large scale dynamic systems under adversarial behaviors. Briefly, uniform and fresh peer sampling guarantees that any node in the system is equally likely to appear as a sample at any non malicious node in the system and that infinitely often any node has a non-null probability to appear as a sample of honest nodes. This sample is built locally out of a stream of node identifiers received at each node. An important issue that seriously hampers the feasibility of node sampling in open and large scale systems is the unavoidable presence of malicious nodes. The objective of malicious nodes mainly consists in continuously and largely biasing the input data stream out of which samples are obtained, to prevent (honest) nodes from being selected as samples. First we demonstrate that restricting the number of requests that malicious nodes can issue and providing a full knowledge of the composition of the system is a necessary and sufficient condition to guarantee uniform and fresh sampling. We also define and study two types of adversary models: an omniscient adversary that has the capacity to eavesdrop on all the messages that are exchanged within the system, and a blind adversary that can only observe messages that have been sent or received by nodes it controls. The former model allows us to derive lower bounds on the impact that the adversary has on the sampling functionality while the latter one corresponds to a more realistic setting. Given any sampling strategy, we quantify the minimum effort exerted by both types of adversary on any input stream to prevent this sampling strategy from outputting a uniform and fresh sample