Time vs. Information Tradeoffs for Leader Election in Anonymous Trees

The leader election task calls for all nodes of a network to agree on a single node. If the nodes of the network are anonymous, the task of leader election is formulated as follows: every node $v$ of the network must output a simple path, coded as a sequence of port numbers, such that all these paths end at a common node, the leader. In this paper, we study deterministic leader election in anonymous trees. Our aim is to establish tradeoffs between the allocated time $\tau$ and the amount of information that has to be given $\textit{a priori}$ to the nodes to enable leader election in time $\tau$ in all trees for which leader election in this time is at all possible. Following the framework of $\textit{algorithms with advice}$, this information (a single binary string) is provided to all nodes at the start by an oracle knowing the entire tree. The length of this string is called the $\textit{size of advice}$. For an allocated time $\tau$, we give upper and lower bounds on the minimum size of advice sufficient to perform leader election in time $\tau$. We consider $n$-node trees of diameter $diam \leq D$. While leader election in time $diam$ can be performed without any advice, for time $diam-1$ we give tight upper and lower bounds of $\Theta (\log D)$. For time $diam-2$ we give tight upper and lower bounds of $\Theta (\log D)$ for even values of $diam$, and tight upper and lower bounds of $\Theta (\log n)$ for odd values of $diam$. For the time interval $[\beta \cdot diam, diam-3]$ for constant $\beta >1/2$, we prove an upper bound of $O(\frac{n\log n}{D})$ and a lower bound of $\Omega(\frac{n}{D})$, the latter being valid whenever $diam$ is odd or when the time is at most $diam-4$. Finally, for time $\alpha \cdot diam$ for any constant $\alpha <1/2$ (except for the case of very small diameters), we give tight upper and lower bounds of $\Theta (n)$

Temporal connectivity of vehicular networks: the power of store-carry-and-forward

Proceeding of: 2015 IEEE Vehicular Networking Conference (VNC), Kyoto, Japan, 16-18 December, 2015Store-carry-and-forward is extensively used in vehicular environments for many and varied purposes, including routing, disseminating, downloading, uploading, or offloading delay-tolerant content. The performance gain of store-carry-and-forward over traditional connected forwarding is primarily determined by the fact that it grants a much improved network connectivity. Indeed, by letting vehicles physically carry data, store-carry-and-forward adds a temporal dimension to the (typically fragmented) instantaneous network topology that is employed by connected forwarding. Temporal connectivity has thus a important role in the operation of a wide range of vehicular network protocols. Still, our understanding of the dynamics of the temporal connectivity of vehicular networks is extremely limited. In this paper, we shed light on this underrated aspect of vehicular networking, by exploring a vast space of scenarios through an evolving graph-theoretical approach. Our results show that using store-carry-and-forward greatly increases connectivity, especially in very sparse networks. Moreover, using store-carry-and-forward mechanisms to share content within a geographically-bounded area can be very efficient, i.e., new entering vehicles can be reached rapidly.This work was done while Marco Gramaglia was at CNR-IEIIT. The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Unions Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n.630211 ReFleX. The work of Christian Glacet was carried out during the tenure of an ERCIM “Alain Bensoussan” Fellowship Programme.Publicad

Disconnected components detection and rooted shortest-path tree maintenance in networks

International audienceMany articles deal with the problem of maintaining a rooted shortest-path tree. However, after some edge deletions, some nodes can be disconnected from the connected component $V_r$ of some distinguished node $r$. In this case, an additional objective is to ensure the detection of the disconnection by the nodes that no longer belong to $V_r$. We present a detailed analysis of a silent self-stabilizing algorithm. We prove that it solves this more demanding task in anonymous weighted networks with the following additional strong properties: it runs without any knowledge on the network and under the \emph{unfair} daemon, that is without any assumption on the asynchronous model. Moreover, it terminates in less than $2n+D$ rounds for a network of $n$ nodes and hop-diameter $D$

Vers un routage compact distribué

International audienceDans cet article, nous proposons plusieurs schémas distribués de routage compact produisant des tables de routage d'au plus O(√n log n) entrées pour un réseau de n nœud, m arêtes et de diamètre D. La complexité de communication de ces algorithmes est de O(nm) et O(nm + n² * log n * min[(√n * log n), D])

Algorithmes de routage (de la réduction des coûts de communication à la dynamique)

Répondre à des requêtes de routage requiert que les entités du réseau, nommées routeurs, aient une connaissance à jour sur la topologie de celui-ci, cette connaissance est appelée table de routage. Le réseau est modélisé par un graphe dans lequel les noeuds représentent les routeurs, et les arêtes les liens de communication entre ceux ci.Cette thèse s intéresse au calcul des tables de routage dans un modèle distribué.Dans ce modèle, les calculs sont effectués par un ensemble de processus placés sur les noeuds. Chaque processus a pour objectif de calculer la table de routage du noeud sur lequel il se trouve. Pour effectuer ce calcul les processus doivent communiquer entre eux. Dans des réseaux de grande taille, et dans le cadre d un calcul distribué, le maintien à jour des tables de routage peut être coûteux en terme de communication. L un des thèmes principaux abordés et celui de la réduction des coûts de communication lors de ce calcul. L une des solutions apportées consisteà réduire la taille des tables de routage, permettant ainsi de réduire les coûts de communication. Cette stratégie classique dans le modèle centralisé est connue sous le nom de routage compact. Cette thèse présente notamment un algorithme de routage compact distribué permettant de réduire significativement les coûts de communication dans les réseaux tels que le réseau internet, i.e. le réseau des systèmes autonomes ainsi que dans des réseaux sans-échelle. Ce document contient également une étude expérimentale de différents algorithmes de routage compact distribués.Enfin, les problèmes liés à la dynamique du réseau sont également abordés. Plusprécisément le reste de l étude porte sur un algorithme auto-stabilisant de calcul d arbre de plus court chemin, ainsi que sur l impact de la suppression de noeuds ou d arêtes sur les tables de routage stockées aux routeurs.In order to respond to routing queries, the entities of the network, nammedrouters, require to have a knowledge concerning the topology of the network, thisknowledge is called routing table. The network is modeled by a graph in whichnodes represent routers and edges represent communication links between nodes.This thesis focuses on routing tables computation in a distributed model. In thismodel, computations are done by a set of process placed on nodes. Every processhas for objective to compute the routing table of the node on which he is placed.To perform this computation, processes have to communicate with each other. Inlarge scale network, in the case of a distributed computation, maintaining routingtables up to date can be costly in terms of communication. This thesis focuses mainlyon the problem of communication cost reduction. One of the solution we proposeis to reduce routing tables size which allow to reduce communication cost. In thecentralised model this strategy is well known under the name of compact routing.This thesis presents in particular a distributed compact routing algorithm that allowsto reduce significantly the communication costs in networks like Internet, i.e. theautonomous systems network and others networks that present scale-free properties.This thesis also contains an experimental study of several distributed compact routingalgorithms. Finally, some problems linked to network dynamicity are addressed.More precisely, the problem of network deconnexion during a shortest path treecomputation with auto-stabilisation guaranties, together with a study of the impactof several edges or nodes deletion on the state of the routing tables.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF

Impact de la dynamique sur la fiabilité d'informations de routage

International audiencePour permettre le routage dans un graphe, les nœuds doivent connaître des portions de route. La dynamique du graphe peut rendre les informations stockées erronées. Cet article s'intéresse à la caractérisation de la quantité d'informations erronées, ainsi qu'aux nombre de changements de distances dans le graphe suite à L suppressions d'arêtes et L' suppressions de nœuds. Nous considérons un graphe G de diamètre D possédant N nœuds et M arêtes. Nous montrons que l'espérance du nombre d'erreurs et de changement de distance est d'au plus D (LN/M + L')

On the Communication Complexity of Distributed Name-Independent Routing Schemes

International audienceWe present a distributed asynchronous algorithm that, for every undirected weighted $n$-node graph $G$, constructs name-independent routing tables for $G$. The size of each table is \tO(\sqrt{n}\,), whereas the length of any route is stretched by a factor of at most~$7$ w.r.t. the shortest path. At any step, the memory space of each node is \tO(\sqrt{n}\,). The algorithm terminates in time $O(D)$, where $D$ is the hop-diameter of $G$. In synchronous scenarios and with uniform weights, it consumes \tO(m\sqrt{n} + n^{3/2}\min\set{D,\sqrt{n}\,}) messages, where $m$ is the number of edges of $G$. In the realistic case of sparse networks of poly-logarithmic diameter, the communication complexity of our scheme, that is \tO(n^{3/2}), improves by a factor of $\sqrt{n}$ the communication complexity of \emph{any} shortest-path routing scheme on the same family of networks. This factor is provable thanks to a new lower bound of independent interest

Algorithme distribué de routage compact en temps optimal

International audienceNous présentons un algorithme distribué construisant des tables de routage de taille sous-linéaire en n, le nombre de nœuds du réseau. Le temps de convergence est proportionnel au diamètre, ce qui est optimal. Par rapport à BGP, la complexité du nombre de messages échangés est améliorée jusqu'à un facteur n^1/2, alors que la longueur des routes induites par les tables est allongée d'un facteur garanti constant. Notre algorithme est conçu pour un environnement statique synchrone ou asynchrone et produit un schéma name-independent

Routing at Large Scale: Advances and Challenges for Complex Networks

International audienceA wide range of social, technological and communication systems can be described as complex networks. Scale-free networks are one of the well-known classes of complex networks in which nodes degree follow a power-law distribution. The design of scalable, adaptive and resilient routing schemes in such networks is very challenging. In this article we present an overview of required routing functionality, categorize the potential design dimensions of routing protocols among existing routing schemes and analyze experimental results and analytical studies performed so far to identify the main trends/trade-offs and draw main conclusions. Besides traditional schemes such as hierarchical/shortest-path path-vector routing, the article pays attention to advances in compact routing and geometric routing since they are known to significantly improve the scalability in terms of memory space. The identified trade-offs and the outcomes of this overview enable more careful conclusions regarding the (in-)suitability of different routing schemes to large-scale complex networks and provide a guideline for future routing research

Routing algorithms : from communication cost reduction to network dynamics

Répondre à des requêtes de routage requiert que les entités du réseau, nommées routeurs, aient une connaissance à jour sur la topologie de celui-ci, cette connaissance est appelée table de routage. Le réseau est modélisé par un graphe dans lequel les noeuds représentent les routeurs, et les arêtes les liens de communication entre ceux ci.Cette thèse s’intéresse au calcul des tables de routage dans un modèle distribué.Dans ce modèle, les calculs sont effectués par un ensemble de processus placés sur les noeuds. Chaque processus a pour objectif de calculer la table de routage du noeud sur lequel il se trouve. Pour effectuer ce calcul les processus doivent communiquer entre eux. Dans des réseaux de grande taille, et dans le cadre d’un calcul distribué, le maintien à jour des tables de routage peut être coûteux en terme de communication. L’un des thèmes principaux abordés et celui de la réduction des coûts de communication lors de ce calcul. L’une des solutions apportées consisteà réduire la taille des tables de routage, permettant ainsi de réduire les coûts de communication. Cette stratégie classique dans le modèle centralisé est connue sous le nom de routage compact. Cette thèse présente notamment un algorithme de routage compact distribué permettant de réduire significativement les coûts de communication dans les réseaux tels que le réseau internet, i.e. le réseau des systèmes autonomes ainsi que dans des réseaux sans-échelle. Ce document contient également une étude expérimentale de différents algorithmes de routage compact distribués.Enfin, les problèmes liés à la dynamique du réseau sont également abordés. Plusprécisément le reste de l’étude porte sur un algorithme auto-stabilisant de calcul d’arbre de plus court chemin, ainsi que sur l’impact de la suppression de noeuds ou d’arêtes sur les tables de routage stockées aux routeurs.In order to respond to routing queries, the entities of the network, nammedrouters, require to have a knowledge concerning the topology of the network, thisknowledge is called routing table. The network is modeled by a graph in whichnodes represent routers and edges represent communication links between nodes.This thesis focuses on routing tables computation in a distributed model. In thismodel, computations are done by a set of process placed on nodes. Every processhas for objective to compute the routing table of the node on which he is placed.To perform this computation, processes have to communicate with each other. Inlarge scale network, in the case of a distributed computation, maintaining routingtables up to date can be costly in terms of communication. This thesis focuses mainlyon the problem of communication cost reduction. One of the solution we proposeis to reduce routing tables size which allow to reduce communication cost. In thecentralised model this strategy is well known under the name of compact routing.This thesis presents in particular a distributed compact routing algorithm that allowsto reduce significantly the communication costs in networks like Internet, i.e. theautonomous systems network and others networks that present scale-free properties.This thesis also contains an experimental study of several distributed compact routingalgorithms. Finally, some problems linked to network dynamicity are addressed.More precisely, the problem of network deconnexion during a shortest path treecomputation with auto-stabilisation guaranties, together with a study of the impactof several edges or nodes deletion on the state of the routing tables