Universal Loop-Free Super-Stabilization

We propose an univesal scheme to design loop-free and super-stabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). Our scheme combines a novel super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree that optimizes a given metric. The composition result preserves the best properties of both worlds: super-stabilization, loop-freedom, and optimization of the original metric without any stabilization time penalty. As case study we apply our composition mechanism to two well known metric-dependent spanning trees: the maximum-flow tree and the minimum degree spanning tree

Construction auto-stabilisante d'un arbre couvrant de poids minimum

International audienceL'arbre couvrant de poids minimum offre une solution de routage ayant le double avantage de donner une structure de communication simple et économique. Dans ce papier, nous présentons un nouvel algorithme auto-stabilisant pour la construction d'un arbre couvrant de poids minimum dans un système distribué et asynchrone. Notre solution améliore l'existant en permettant d'atteindre un meilleur compromis entre le temps de convergence, $O(n^2)$, et la complexité en mémoire nécessaire sur chaque noeud du réseau, $O(\log^2 n)$. Le temps de convergence est amélioré d'un facteur multiplicatif $\Theta(n)$ au prix d'un facteur multiplicatif de $O(\log n)$ sur la mémoire. La clé de voûte de ce travail est l'utilisation d'une méthode de nommage auto-stabilisante permettant d'identifier pour toute paire de noeuds le plus proche ancêtre commun dans l'arbre

Communication Efficient Self-Stabilizing Leader Election

This paper presents a randomized self-stabilizing algorithm that elects a leader r in a general n-node undirected graph and constructs a spanning tree T rooted at r. The algorithm works under the synchronous message passing network model, assuming that the nodes know a linear upper bound on n and that each edge has a unique ID known to both its endpoints (or, alternatively, assuming the KT? model). The highlight of this algorithm is its superior communication efficiency: It is guaranteed to send a total of O? (n) messages, each of constant size, till stabilization, while stabilizing in O? (n) rounds, in expectation and with high probability. After stabilization, the algorithm sends at most one constant size message per round while communicating only over the (n - 1) edges of T. In all these aspects, the communication overhead of the new algorithm is far smaller than that of the existing (mostly deterministic) self-stabilizing leader election algorithms. The algorithm is relatively simple and relies mostly on known modules that are common in the fault free leader election literature; these modules are enhanced in various subtle ways in order to assemble them into a communication efficient self-stabilizing algorithm

A new self-stabilizing minimum spanning tree construction with loop-free property

International audienceThe minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner. The loop-free property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol. We present a new self-stabilizing MST protocol that improves on previous known approaches in several ways. First, it makes fewer system hypotheses as the size of the network (or an upper bound on the size) need not be known to the participants. Second, it is loop-free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new MST. Finally, time complexity matches the best known results, while space complexity results show that this protocol is the most efficient to date

A New Self-Stabilizing Minimum Spanning Tree Construction with Loop-Free Property

International audienceThe minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner. The loop-free property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol. We present a new self-stabilizing MST protocol that improves on previous known approaches in several ways. First, it makes fewer system hypotheses as the size of the network (or an upper bound on the size) need not be known to the participants. Secondly, it is loop-free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new MST. Finally, time complexity matches the best known results, while space complexity results show that this protocol is the most efficient to date

Fast and compact self-stabilizing verification, computation, and fault detection of an MST

This paper demonstrates the usefulness of distributed local verification of proofs, as a tool for the design of self-stabilizing algorithms.In particular, it introduces a somewhat generalized notion of distributed local proofs, and utilizes it for improving the time complexity significantly, while maintaining space optimality. As a result, we show that optimizing the memory size carries at most a small cost in terms of time, in the context of Minimum Spanning Tree (MST). That is, we present algorithms that are both time and space efficient for both constructing an MST and for verifying it.This involves several parts that may be considered contributions in themselves.First, we generalize the notion of local proofs, trading off the time complexity for memory efficiency. This adds a dimension to the study of distributed local proofs, which has been gaining attention recently. Specifically, we design a (self-stabilizing) proof labeling scheme which is memory optimal (i.e., $O(\log n)$ bits per node), and whose time complexity is $O(\log ^2 n)$ in synchronous networks, or $O(\Delta \log ^3 n)$ time in asynchronous ones, where $\Delta$ is the maximum degree of nodes. This answers an open problem posed by Awerbuch and Varghese (FOCS 1991). We also show that $\Omega(\log n)$ time is necessary, even in synchronous networks. Another property is that if $f$ faults occurred, then, within the requireddetection time above, they are detected by some node in the $O(f\log n)$ locality of each of the faults.Second, we show how to enhance a known transformer that makes input/output algorithms self-stabilizing. It now takes as input an efficient construction algorithm and an efficient self-stabilizing proof labeling scheme, and produces an efficient self-stabilizing algorithm. When used for MST, the transformer produces a memory optimal self-stabilizing algorithm, whose time complexity, namely, $O(n)$, is significantly better even than that of previous algorithms. (The time complexity of previous MST algorithms that used $\Omega(\log^2 n)$ memory bits per node was $O(n^2)$, and the time for optimal space algorithms was $O(n|E|)$.) Inherited from our proof labelling scheme, our self-stabilising MST construction algorithm also has the following two properties: (1) if faults occur after the construction ended, then they are detected by some nodes within $O(\log ^2 n)$ time in synchronous networks, or within $O(\Delta \log ^3 n)$ time in asynchronous ones, and (2) if $f$ faults occurred, then, within the required detection time above, they are detected within the $O(f\log n)$ locality of each of the faults. We also show how to improve the above two properties, at the expense of some increase in the memory