Agrégation Distribuée de Données dans les Réseaux Dynamiques

International audienceL'agrégation de données dans un réseau est un problème central pour de nombreuses applications. Il consiste a récupérer les données de chaque noeud du réseau, en supposant que deux données peuvent être agrégées en une seule, et que chaque noeud ne transmet une donnée qu'une seule fois. Des solutions distribuées performantes (du point de vue du délai) existent dans le cas d'un réseau statique, même en présence de collisions (comme dans les réseaux de capteurs sans fil). Cependant, dans le cas des réseaux dynamiques, le problème est NP-difficile, même avec un algorithme centralisé qui connait l'évolution future du réseau. Dans cet article, nous étudions le problème de l'agrégation de données dans des réseaux dynamiques par un algorithme distribué, dans le cas où il n'y a pas de collisions. Après avoir défini formellement le problème, nous prouvons qu'il n'est pas solvable sans connaissance supplémentaire, face à un adversaire sans mémoire, et ce même avec un algorithme probabiliste. Ensuite, nous étudions le problème face à un adversaire probabiliste choisissant les interactions dans le réseau de manière aléatoire. Dans ce cas nous donnons des algorithmes optimaux utilisant (i) une connaissance partielle du future ou (ii) aucune connaissance

Distributed Online Data Aggregation in Dynamic Graphs

We consider the problem of aggregating data in a dynamic graph, that is, aggregating the data that originates from all nodes in the graph to a specific node, the sink. We are interested in giving lower bounds for this problem, under different kinds of adversaries. In our model, nodes are endowed with unlimited memory and unlimited computational power. Yet, we assume that communications between nodes are carried out with pairwise interactions, where nodes can exchange control information before deciding whether they transmit their data or not, given that each node is allowed to transmit its data at most once. When a node receives a data from a neighbor, the node may aggregate it with its own data. We consider three possible adversaries: the online adaptive adversary, the oblivious adversary , and the randomized adversary that chooses the pairwise interactions uniformly at random. For the online adaptive and the oblivious adversary, we give impossibility results when nodes have no knowledge about the graph and are not aware of the future. Also, we give several tight bounds depending on the knowledge (be it topology related or time related) of the nodes. For the randomized adversary, we show that the Gathering algorithm, which always commands a node to transmit, is optimal if nodes have no knowledge at all. Also, we propose an algorithm called Waiting Greedy, where a node either waits or transmits depending on some parameter, that is optimal when each node knows its future pairwise interactions with the sink

The Complexity of Data Aggregation in Static and Dynamic Wireless Sensor Networks

International audienceThe key feature of wireless sensor networks is to aggregate data collected by individual sensors in an energy efficient manner. We consider two techniques to save energy. The first one is to avoid collisions due to simultaneous transmissions among neighboring nodes. Second, when a node receives data from multiple neighbors, it aggregates these with its own data. Then, one transmission is sufficient to transmit all consolidated data to another neighbor. If the overall delay has to be kept as low as possible, scheduling sensors to avoid collisions while aggregating data becomes challenging.The contribution of this paper is threefold. First, we give tight bounds for the complexity of data aggregation in static networks. In more details, we show that the problem remains NP-complete when the graph is of degree at most three. As it is trivial to solve the problem in static graphs of degree at most two, our result implies that the problem is intrinsically difficult for any practical setting. Second, we investigate the complexity of the same problem in a dynamic network, that is, a network whose topology can evolve through time. In the case of dynamic networks, we show that the problem is NP-complete even in the case where the graph is of degree at most two (and it is trivial to solve the problem when the graph is of degree at most one). Third, we give the first lower and upper bounds for the minimum data aggregation time in a dynamic graph.We observe that even in a well-connected evolving graphs, the optimal solution cannot be found by a distributed algorithm or by a centralized algorithm that does not know the future. Thus we finally give the first approximation algorithm (centralized that knows the future) whose approximation factor is T(n−1) if there exists a bound T such that there is a journey (a path in a dynamic graph) for all pairs of nodes in every time interval [t,t+T]