Self-stabilizing tree algorithms

Designers of distributed algorithms have to contend with the problem of making the algorithms tolerant to several forms of coordination loss, primarily faulty initialization. The processes in a distributed system do not share a global memory and can only get a partial view of the global state. Transient failures in one part of the system may go unnoticed in other parts and thus cause the system to go into an illegal state. If the system were self-stabilizing, however, it is guaranteed that it will return to a legal state after a finite number of state transitions. This thesis presents and proves self-stabilizing algorithms for calculating tree metrics and for achieving mutual exclusion on a tree structured distributed system

Self-Stabilization in the Distributed Systems of Finite State Machines

The notion of self-stabilization was first proposed by Dijkstra in 1974 in his classic paper. The paper defines a system as self-stabilizing if, starting at any, possibly illegitimate, state the system can automatically adjust itself to eventually converge to a legitimate state in finite amount of time and once in a legitimate state it will remain so unless it incurs a subsequent transient fault. Dijkstra limited his attention to a ring of finite-state machines and provided its solution for self-stabilization. In the years following his introduction, very few papers were published in this area. Once his proposal was recognized as a milestone in work on fault tolerance, the notion propagated among the researchers rapidly and many researchers in the distributed systems diverted their attention to it. The investigation and use of self-stabilization as an approach to fault-tolerant behavior under a model of transient failures for distributed systems is now undergoing a renaissance. A good number of works pertaining to self-stabilization in the distributed systems were proposed in the yesteryears most of which are very recent. This report surveys all previous works available in the literature of self-stabilizing systems

Weak vs. Self vs. Probabilistic Stabilization

Self-stabilization is a strong property that guarantees that a network always resume correct behavior starting from an arbitrary initial state. Weaker guarantees have later been introduced to cope with impossibility results: probabilistic stabilization only gives probabilistic convergence to a correct behavior. Also, weak stabilization only gives the possibility of convergence. In this paper, we investigate the relative power of weak, self, and probabilistic stabilization, with respect to the set of problems that can be solved. We formally prove that in that sense, weak stabilization is strictly stronger that self-stabilization. Also, we refine previous results on weak stabilization to prove that, for practical schedule instances, a deterministic weak-stabilizing protocol can be turned into a probabilistic self-stabilizing one. This latter result hints at more practical use of weak-stabilization, as such algorthms are easier to design and prove than their (probabilistic) self-stabilizing counterparts

Maximum Matching for Anonymous Trees with Constant Space per Process

We give a silent self-stabilizing protocol for computing a maximum matching in an anonymous network with a tree topology. The round complexity of our protocol is O(diam), where diam is the diameter of the network, and the step complexity is O(n*diam), where n is the number of processes in the network. The working space complexity is O(1) per process, although the output necessarily takes O(log(delta)) space per process, where delta is the degree of that process. To implement parent pointers in constant space, regardless of degree, we use the cyclic Abelian group Z_7

Memory requirements for silent stabilization

A self-stabilizing algorithm is silent if it converges to a glc)bal state after which the values stored in the com-munication registers are fixed. The silence property of self-stabilizing algorithms is a desirable property in terms of simplicity and communication overhead. In this work we show that no constant memory silent self-stabilizing algorithms exist for identification of the centers of a graph, leader election, and spanning tree construction. Lower bounds of Cl(log n) bits per communication register are obtained for each of the above tasks. The existence of a silent legitimate global state that uses less than log n bits per register is assumed. This legitimate global state is used to construct a silent global state that is illegitimate.

Découverte et allocation des ressources pour le traitement de requêtes dans les systèmes grilles

De nos jours, les systèmes Grille, grâce à leur importante capacité de calcul et de stockage ainsi que leur disponibilité, constituent l'un des plus intéressants environnements informatiques. Dans beaucoup de différents domaines, on constate l'utilisation fréquente des facilités que les environnements Grille procurent. Le traitement des requêtes distribuées est l'un de ces domaines où il existe de grandes activités de recherche en cours, pour transférer l'environnement sous-jacent des systèmes distribués et parallèles à l'environnement Grille. Dans le cadre de cette thèse, nous nous concentrons sur la découverte des ressources et des algorithmes d'allocation de ressources pour le traitement des requêtes dans les environnements Grille. Pour ce faire, nous proposons un algorithme de découverte des ressources pour le traitement des requêtes dans les systèmes Grille en introduisant le contrôle de topologie auto-stabilisant et l'algorithme de découverte des ressources dirigé par l'élection convergente. Ensuite, nous présentons un algorithme d'allocation des ressources, qui réalise l'allocation des ressources pour les requêtes d'opérateur de jointure simple par la génération d'un espace de recherche réduit pour les nœuds candidats et en tenant compte des proximités des candidats aux sources de données. Nous présentons également un autre algorithme d'allocation des ressources pour les requêtes d'opérateurs de jointure multiple. Enfin, on propose un algorithme d'allocation de ressources, qui apporte une tolérance aux pannes lors de l'exécution de la requête par l'utilisation de la réplication passive d'opérateurs à état. La contribution générale de cette thèse est double. Premièrement, nous proposons un nouvel algorithme de découverte de ressource en tenant compte des caractéristiques des environnements Grille. Nous nous adressons également aux problèmes d'extensibilité et de dynamicité en construisant une topologie efficace sur l'environnement Grille et en utilisant le concept d'auto-stabilisation, et par la suite nous adressons le problème de l'hétérogénéité en proposant l'algorithme de découverte de ressources dirigé par l'élection convergente. La deuxième contribution de cette thèse est la proposition d'un nouvel algorithme d'allocation des ressources en tenant compte des caractéristiques de l'environnement Grille. Nous abordons les problèmes causés par la grande échelle caractéristique en réduisant l'espace de recherche pour les ressources candidats. De ce fait nous réduisons les coûts de communication au cours de l'exécution de la requête en allouant des nœuds au plus près des sources de données. Et enfin nous traitons la dynamicité des nœuds, du point de vue de leur existence dans le système, en proposant un algorithme d'affectation des ressources avec une tolérance aux pannes.Grid systems are today's one of the most interesting computing environments because of their large computing and storage capabilities and their availability. Many different domains profit the facilities of grid environments. Distributed query processing is one of these domains in which there exists large amounts of ongoing research to port the underlying environment from distributed and parallel systems to the grid environment. In this thesis, we focus on resource discovery and resource allocation algorithms for query processing in grid environments. For this, we propose resource discovery algorithm for query processing in grid systems by introducing self-stabilizing topology control and converge-cast based resource discovery algorithms. Then, we propose a resource allocation algorithm, which realizes allocation of resources for single join operator queries by generating a reduced search space for the candidate nodes and by considering proximities of candidates to the data sources. We also propose another resource allocation algorithm for queries with multiple join operators. Lastly, we propose a fault-tolerant resource allocation algorithm, which provides fault-tolerance during the execution of the query by the use of passive replication of stateful operators. The general contribution of this thesis is twofold. First, we propose a new resource discovery algorithm by considering the characteristics of the grid environments. We address scalability and dynamicity problems by constructing an efficient topology over the grid environment using the self-stabilization concept; and we deal with the heterogeneity problem by proposing the converge-cast based resource discovery algorithm. The second main contribution of this thesis is the proposition of a new resource allocation algorithm considering the characteristics of the grid environment. We tackle the scalability problem by reducing the search space for candidate resources. We decrease the communication costs during the query execution by allocating nodes closer to the data sources. And finally we deal with the dynamicity of nodes, in terms of their existence in the system, by proposing the fault-tolerant resource allocation algorithm

A self-stabilizing distributed maximum flow algorithm

This thesis presents a self-stabilizing distributed maximum flow algorithm for a network G = (V, E), where V is a set of nodes in the network and E is a set of edges in the network. The algorithm has two phases: reset phase and preflow-push phase. Fault-tolerance is achieved by using a self-stabilizing paradigm that uses non-masking fault-tolerance embedded repetitions within the algorithm. Two techniques are used in the algorithm, Counter flushing is used to synchronize the network; both local checking and local correction are used to compute the maximum flow of the network. The algorithm handles catastrophic faults by weeding out false information in the network. A network can start with any arbitrary global state and will recover to a legal global state in finite number of steps. Lastly, the network guarantees to restore the legal configuration from any catastrophic faults

The (k,l) Coredian tree for Ad Hoc Networks

In this paper, we present a new efficient strategy for constructing a wireless tree network containing n nodes of diameter ∆ while satisfying the QoS requirements such as bandwidth and delay. Given a tree network T , a coredian path is a path in T that minimizes the centdian function, a k-coredian tree is a subtree of T with k leaves that minimizes the centdian function, and a (k, l)-coredian tree is a subtree of T with k leaves and diameter l at most that minimizes the centdian function. The (k, l)-coredian tree can serve as a backbone for a network, where the internal nodes belong to the backbone and the leaves serve as the heads of the clusters covering the rest of the network. We show that a coredian path can be constructed at O(∆) time with O(n) messages and a k-coredian tree can be constructed at O(k∆) time with O(kn) messages. We provide an O(n 2 ) time construction algorithm for the (k, l)-coredian tree that requires O(n 2 ) messages. We also give upper and lower bounds for a number of nodes covered by the k cluster heads in random geometric graph using critical transmission range of connected network. Finally, simulation is presented for various values of n and k

Center location problems on tree graphs with subtree-shaped customers

We consider the p-center problem on tree graphs where the customers are modeled as continua subtrees. We address unweighted and weighted models as well as distances with and without addends. We prove that a relatively simple modification of Handler’s classical linear time algorithms for unweighted 1- and 2-center problems with respect to point customers, linearly solves the unweighted 1- and 2-center problems with addends of the above subtree customer model. We also develop polynomial time algorithms for the p-center problems based on solving covering problems and searching over special domains