Connectivity preserving network transformers

The Population Protocol model is a distributed model that concerns systems of very weak computational entities that cannot control the way they interact. The model of Network Constructors is a variant of Population Protocols capable of (algorithmically) constructing abstract networks. Both models are characterized by a fundamental inability to terminate. In this work, we investigate the minimal strengthenings of the latter that could overcome this inability. Our main conclusion is that initial connectivity of the communication topology combined with the ability of the protocol to transform the communication topology plus a few other local and realistic assumptions are sufficient to guarantee not only termination but also the maximum computational power that one can hope for in this family of models. The technique is to transform any initial connected topology to a less symmetric and detectable topology without ever breaking its connectivity during the transformation. The target topology of all of our transformers is the spanning line and we call Terminating Line Transformation the corresponding problem. We first study the case in which there is a pre-elected unique leader and give a time-optimal protocol for Terminating Line Transformation. We then prove that dropping the leader without additional assumptions leads to a strong impossibility result. In an attempt to overcome this, we equip the nodes with the ability to tell, during their pairwise interactions, whether they have at least one neighbor in common. Interestingly, it turns out that this local and realistic mechanism is sufficient to make the problem solvable. In particular, we give a very efficient protocol that solves Terminating Line Transformation when all nodes are initially identical. The latter implies that the model computes with termination any symmetric predicate computable by a Turing Machine of space $\Theta(n^2)$

A Taxonomy of Daemons in Self-stabilization

We survey existing scheduling hypotheses made in the literature in self-stabilization, commonly referred to under the notion of daemon. We show that four main characteristics (distribution, fairness, boundedness, and enabledness) are enough to encapsulate the various differences presented in existing work. Our naming scheme makes it easy to compare daemons of particular classes, and to extend existing possibility or impossibility results to new daemons. We further examine existing daemon transformer schemes and provide the exact transformed characteristics of those transformers in our taxonomy.Comment: 26 page

A New Self-Stabilizing Maximal Matching Algorithm

The maximal matching problem has received considerable attention in the self-stabilizing community. Previous work has given different self-stabilizing algorithms that solves the problem for both the adversarial and fair distributed daemon, the sequential adversarial daemon, as well as the synchronous daemon. In the following we present a single self-stabilizing algorithm for this problem that unites all of these algorithms in that it stabilizes in the same number of moves as the previous best algorithms for the sequential adversarial, the distributed fair, and the synchronous daemon. In addition, the algorithm improves the previous best moves complexities for the distributed adversarial daemon from O(n^2) and O(delta m) to O(m) where n is the number of processes, m is thenumber of edges, and delta is the maximum degree in the graph

Supercomputing futures : the next sharing paradigm for HPC resources : economic model, market analysis and consequences for the Grid

À la croisée des chemins du génie informatique, de la finance et de l'économétrie, cette thèse se veut fondamentalement un exercice en ingénierie économique dont l' objectif est de contribuer un système novateur, durable et adaptatif pour le partage de resources de calcul haute-performance. Empruntant à la finance fondamentale et à l'analyse technique, le modèle proposé construit des ratios et des indices de marché à partir de statistiques transactionnelles. Cette approche, encourageant les comportements stratégiques, pave la voie à une métaphore de partage plus efficace pour la Grid, où l'échange de ressources se voit maintenant pondéré. Le concept de monnaie de Grid, un instrument beaucoup plus liquide et utilisable que le troc de resources comme telles est proposé: les Grid Credits. Bien que les indices proposés ne doivent pas être considérés comme des indicateurs absolus et contraignants, ils permettent néanmoins aux négociants de se faire une idée de la valeur au marché des différentes resources avant de se positionner. Semblable sur de multiples facettes aux bourses de commodités, le Grid Exchange, tel que présenté, permet l'échange de resources via un mécanisme de double-encan. Néanmoins, comme les resources de super-calculateurs n'ont rien de standardisé, la plate-forme permet l'échange d'ensemble de commodités, appelés requirement sets, pour les clients, et component sets, pour les fournisseurs. Formellement, ce modèle économique n'est qu'une autre instance de la théorie des jeux non-coopératifs, qui atteint éventuellement ses points d'équilibre. Suivant les règles du "libre-marché", les utilisateurs sont encouragés à spéculer, achetant, ou vendant, à leur bon vouloir, l'utilisation des différentes composantes de superordinateurs. En fin de compte, ce nouveau paradigme de partage de resources pour la Grid dresse la table à une nouvelle économie et une foule de possibilités. Investissement et positionnement stratégique, courtiers, spéculateurs et même la couverture de risque technologique sont autant d'avenues qui s'ouvrent à l'horizon de la recherche dans le domaine