Optimal Gossip Algorithms for Exact and Approximate Quantile Computations

This paper gives drastically faster gossip algorithms to compute exact and approximate quantiles. Gossip algorithms, which allow each node to contact a uniformly random other node in each round, have been intensely studied and been adopted in many applications due to their fast convergence and their robustness to failures. Kempe et al. [FOCS'03] gave gossip algorithms to compute important aggregate statistics if every node is given a value. In particular, they gave a beautiful $O(\log n + \log \frac{1}{\epsilon})$ round algorithm to $\epsilon$-approximate the sum of all values and an $O(\log^2 n)$ round algorithm to compute the exact $\phi$-quantile, i.e., the the $\lceil \phi n \rceil$ smallest value. We give an quadratically faster and in fact optimal gossip algorithm for the exact $\phi$-quantile problem which runs in $O(\log n)$ rounds. We furthermore show that one can achieve an exponential speedup if one allows for an $\epsilon$-approximation. We give an $O(\log \log n + \log \frac{1}{\epsilon})$ round gossip algorithm which computes a value of rank between $\phi n$ and $(\phi+\epsilon)n$ at every node.% for any $0 \leq \phi \leq 1$ and $0 < \epsilon < 1$. Our algorithms are extremely simple and very robust - they can be operated with the same running times even if every transmission fails with a, potentially different, constant probability. We also give a matching $\Omega(\log \log n + \log \frac{1}{\epsilon})$ lower bound which shows that our algorithm is optimal for all values of $\epsilon$

Improving Message Dissemination in Opportunistic Networks

Data transmission has become a need in various fields, like in social networks with the diverse interaction applications, or in the scientific and engineering areas where for example the use of sensors to capture data is growing, or in emergency situations where there is the imperative need to have a communication system to coordinate rescue operations. Wireless networks have been able to solve these issues to a great extent, but what can we do when a fixed supporting infrastructure is not available or becomes inoperative because of saturation? Opportunistic wireless networks are an alternative to consider in these situations, since their operation does not depend on the existence of a telecommunications infrastructure but they provide connectivity through the organized cooperation of users. This research thesis focuses on these types of networks and is aimed at improving the dissemination of information in opportunistic networks analyzing the main causes that influence the performance of data transmission. Opportunistic networks do not depend on a fixed topology but depend on the number and mobility of users, the type and quantity of information generated and sent, as well as the physical characteristics of the mobile devices that users have to transmit the data. The combination of these elements impacts on the duration of the contact time between mobile users, directly affecting the information delivery probability. This thesis starts by presenting a thorough "state of the art" study where we present the most important contributions related to this area and the solutions offered for the evaluation of the opportunistic networks, such as simulation models, routing protocols, simulation tools, among others. After offering this broad background, we evaluate the consumption of the resources of the mobile devices that affect the performance of the the applications of opportunistic networks, both from the energetic and the memory point of view. Next, we analyze the performance of opportunistic networks considering either pedestrian and vehicular environments. The studied approaches include the use of additional fixed nodes and different data transmission technologies, to improve the duration of the contact between mobile devices. Finally, we propose a diffusion scheme to improve the performance of data transmission based on extending the duration of the contact time and the likelihood that users will collaborate in this process. This approach is complemented by the efficient management of the resources of the mobile devices.La transmisión de datos se ha convertido en una necesidad en diversos ámbitos, como en las redes sociales con sus diversas aplicaciones, o en las áreas científicas y de ingeniería donde, por ejemplo, el uso de sensores para capturar datos está creciendo, o en situaciones de emergencia donde impera la necesidad de tener un sistema de comunicación para coordinar las operaciones de rescate. Las redes inalámbricas actuales han sido capaces de resolver estos problemas en gran medida, pero ¿qué podemos hacer cuando una infraestructura de soporte fija no está disponible o estas se vuelven inoperantes debido a la saturación de peticiones de red? Las redes inalámbricas oportunísticas son una alternativa a considerar en estas situaciones, ya que su funcionamiento no depende de la existencia de una infraestructura de telecomunicaciones sino que la conectividad es a través de la cooperación organizada de los usuarios. Esta tesis de investigación se centra en estos tipos de redes oportunísticas y tiene como objetivo mejorar la difusión de información analizando las principales causas que influyen en el rendimiento de la transmisión de datos. Las redes oportunísticas no dependen de una topología fija, sino que dependen del número y la movilidad de los usuarios, del tipo y cantidad de información generada y enviada, así como de las características físicas de los dispositivos móviles que los usuarios tienen para transmitir los datos. La combinación de estos elementos influye en la duración del tiempo de contacto entre usuarios móviles, afectando directamente a la probabilidad de entrega de información. Esta tesis comienza presentando un exhaustivo estudio del ``estado del arte", donde presentamos las contribuciones más importantes relacionadas con esta área y las soluciones existentes para la evaluación de las redes oportunísticas, tales como modelos de simulación, protocolos de enrutamiento, herramientas de simulación, entre otros. Tras ofrecer esta amplia compilación de investigaciones, se evalúa el consumo de recursos de los dispositivos móviles que afectan al rendimiento de las aplicaciones de redes oportunísticas, desde el punto de vista energético así como de la memoria. A continuación, analizamos el rendimiento de las redes oportunísticas considerando tanto los entornos peatonales como vehiculares. Los enfoques estudiados incluyen el uso de nodos fijos adicionales y diferentes tecnologías de transmisión de datos, para mejorar la duración del contacto entre dispositivos móviles. Finalmente, proponemos un esquema de difusión para mejorar el rendimiento de la transmisión de datos basado en la extensión de la duración del tiempo de contacto, y de la probabilidad de que los usuarios colaboren en este proceso. Este enfoque se complementa con la gestión eficiente de los recursos de los dispositivos móviles.La transmissió de dades s'ha convertit en una necessitat en diversos àmbits, com ara en les xarxes socials amb les diverses aplicacions d'interacció, o en les àrees científiques i d'enginyeria, en les quals, per exemple, l'ús de sensors per a capturar dades creix en l'actualitat, o en situacions d'emergència en què impera la necessitat de tenir un sistema de comunicació per a coordinar les operacions de rescat. Les xarxes sense fil han sigut capaces de resoldre aquests problemes en gran manera, però què podem fer quan una infraestructura de suport fixa no està disponible, o bé aquestes es tornen inoperants a causa de la saturació de peticions de xarxa? Les xarxes sense fil oportunistes són una alternativa que cal considerar en aquestes situacions, ja que el funcionament d'aquestes xarxes no depèn de l'existència d'una infraestructura de telecomunicacions, sinó que la connectivitat s'hi aconsegueix a través de la cooperació organitzada dels usuaris. Aquesta tesi de recerca se centra en aquest tipus de xarxes, i té com a objectiu millorar la difusió d'informació en xarxes oportunistes tot analitzant les principals causes que influeixen en el rendiment de la transmissió de dades. Les xarxes oportunistes no depenen d'una topologia fixa, sinó del nombre i la mobilitat dels usuaris, del tipus i la quantitat d'informació generada i enviada, i de les característiques físiques dels dispositius mòbils que els usuaris tenen per a transmetre les dades. La combinació d'aquests elements influeix en la durada del temps de contacte entre usuaris mòbils, i afecta directament la probabilitat de lliurament d'informació. Aquesta tesi comença amb un estudi exhaustiu de l'estat de la qüestió, en què presentem les contribucions més importants relacionades amb aquesta àrea i les solucions oferides per a l'avaluació de les xarxes oportunistes, com ara models de simulació, protocols d'encaminament o eines de simulació, entre d'altres. Després de mostrar aquest ampli panorama, s'avalua el consum dels recursos dels dispositius mòbils que afecten l'acompliment de les aplicacions de xarxes oportunistes, tant des del punt de vista energètic com de la memòria. A continuació, analitzem l'acompliment de xarxes oportunistes considerant tant els entorns de vianants com els vehiculars. Els enfocaments estudiats inclouen l'ús de nodes fixos addicionals i diferents tecnologies de transmissió de dades per a millorar la durada del contacte entre dispositius mòbils. Finalment, proposem un esquema de difusió per a millorar el rendiment de la transmissió de dades basat en l'extensió de la durada del temps de contacte, i de la probabilitat que els usuaris col·laboren en aquest procés. Aquest enfocament es complementa amb la gestió eficient dels recursos dels dispositius mòbils.Herrera Tapia, J. (2017). Improving Message Dissemination in Opportunistic Networks [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86129TESI

Randomized and efficient time synchronization in dynamic wireless sensor networks: a gossip-consensus-based approach

This paper proposes novel randomized gossip-consensus-based sync (RGCS) algorithms to realize efficient time correction in dynamic wireless sensor networks (WSNs). First, the unreliable links are described by stochastic connections, reflecting the characteristic of changing connectivity gleaned from dynamicWSNs. Secondly, based on the mutual drift estimation, each pair of activated nodes fully adjusts clock rate and offset to achieve network-wide time synchronization by drawing upon the gossip consensus approach. The converge-to-max criterion is introduced to achieve a much faster convergence speed. The theoretical results on the probabilistic synchronization performance of the RGCS are presented. Thirdly, a Revised-RGCS is developed to counteract the negative impact of bounded delays, because the uncertain delays are always present in practice and would lead to a large deterioration of algorithm performances. Finally, extensive simulations are performed on the MATLAB and OMNeT++ platform for performance evaluation. Simulation results demonstrate that the proposed algorithms are not only efficient for synchronization issues required for dynamic topology changes but also give a better performance in term of converging speed, collision rate, and the robustness of resisting delay, and outperform other existing protocols

Probabilistic methods for distributed information dissemination

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 457-484).The ever-increasing growth of modern networks comes with a paradigm shift in network operation. Networks can no longer be abstracted as deterministic, centrally controlled systems with static topologies but need to be understood as highly distributed, dynamic systems with inherent unreliabilities. This makes many communication, coordination and computation tasks challenging and in many scenarios communication becomes a crucial bottleneck. In this thesis, we develop new algorithms and techniques to address these challenges. In particular we concentrate on broadcast and information dissemination tasks and introduce novel ideas on how randomization can lead to powerful, simple and practical communication primitives suitable for these modern networks. In this endeavor we combine and further develop tools from different disciplines trying to simultaneously addresses the distributed, information theoretic and algorithmic aspects of network communication. The two main probabilistic techniques developed to disseminate information in a network are gossip and random linear network coding. Gossip is an alternative to classical flooding approaches: Instead of nodes repeatedly forwarding information to all their neighbors, gossiping nodes forward information only to a small number of (random) neighbors. We show that, when done right, gossip disperses information almost as quickly as flooding, albeit with a drastically reduced communication overhead. Random linear network coding (RLNC) applies when a large amount of information or many messages are to be disseminated. Instead of routing messages through intermediate nodes, that is, following a classical store-and-forward approach, RLNC mixes messages together by forwarding random linear combinations of messages. The simplicity and topology-obliviousness of this approach makes RLNC particularly interesting for the distributed settings considered in this thesis. Unfortunately the performance of RLNC was not well understood even for the simplest such settings. We introduce a simple yet powerful analysis technique that allows us to prove optimal performance guarantees for all settings considered in the literature and many more that were not analyzable so far. Specifically, we give many new results for RLNC gossip algorithms, RLNC algorithms for dynamic networks, and RLNC with correlated data. We also provide a novel highly efficient distributed implementation of RLNC that achieves these performance guarantees while buffering only a minimal amount of information at intermediate nodes. We then apply our techniques to improve communication primitives in multi-hop radio networks. While radio networks inherently support broadcast communications, e.g., from one node to all surrounding nodes, interference of simultaneous transmissions makes multihop broadcast communication an interesting challenge. We show that, again, randomization holds the key for obtaining simple, efficient and distributed information dissemination protocols. In particular, using random back-off strategies to coordinate access to the shared medium leads to optimal gossip-like communications and applying RLNC achieves the first throughput-optimal multi-message communication primitives. Lastly we apply our probabilistic approach for analyzing simple, distributed propagation protocols in a broader context by studying algorithms for the Lovász Local Lemma. These algorithms find solutions to certain local constraint satisfaction problems by randomly fixing and propagating violations locally. Our two main results show that, firstly, there are also efficient deterministic propagation strategies achieving the same and, secondly, using the random fixing strategy has the advantage of producing not just an arbitrary solution but an approximately uniformly random one. Both results lead to simple, constructions for a many locally consistent structures of interest that were not known to be efficiently constructable before.by Bernhard Haeupler.Ph.D