Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots

We consider a team of $k$ identical, oblivious, asynchronous mobile robots that are able to sense (\emph{i.e.}, view) their environment, yet are unable to communicate, and evolve on a constrained path. Previous results in this weak scenario show that initial symmetry yields high lower bounds when problems are to be solved by \emph{deterministic} robots. In this paper, we initiate research on probabilistic bounds and solutions in this context, and focus on the \emph{exploration} problem of anonymous unoriented rings of any size. It is known that $\Theta(\log n)$ robots are necessary and sufficient to solve the problem with $k$ deterministic robots, provided that $k$ and $n$ are coprime. By contrast, we show that \emph{four} identical probabilistic robots are necessary and sufficient to solve the same problem, also removing the coprime constraint. Our positive results are constructive

Self-Stabilizing Distributed Cooperative Reset

Self-stabilization is a versatile fault-tolerance approach that characterizes the ability of a system to eventually resume a correct behavior after any finite number of transient faults. In this paper, we propose a self-stabilizing reset algorithm working in anonymous networks. This algorithm resets the network in a distributed non-centralized manner, i.e., it is multi-initiator, as each process detecting an inconsistency may initiate a reset. It is also cooperative in the sense that it coordinates concurrent reset executions in order to gain efficiency. Our approach is general since our reset algorithm allows to build self-stabilizing solutions for various problems and settings. As a matter of facts, we show that it applies to both static and dynamic specifications since we propose efficient self-stabilizing reset-based algorithms for the (1-minimal) (f, g)-alliance (a generalization of the dominating set problem) in identified networks and the unison problem in anonymous networks. Notice that these two latter instantiations enhance the state of the art. Indeed, in the former case, our solution is more general than the previous ones, while in the latter case, the complexity of our unison algorithm is better than that of previous solutions of the literature

Stabilisation Instantanée Probabiliste

International audienceNous introduisons la stabilisation instantanée probabiliste. Cette propriété nous permet, en particulier, de concevoir des algorithmes distribués pour réseaux anonymes ayant de fortes propriétés de tolérance aux pannes transitoires. Un algorithme instantanément stabilisant probabiliste satisfait la sûreté de sa spécification immédiatement après que les pannes transitoires aient cessé; cependant il n'assure la vivacité de sa spécification que presque sûrement. Nous illustrons cette nouvelle propriété en proposant deux algorithmes instantanément stabilisants probabilistes d'élection avec garantie de service pour réseaux anonymes, ce problème n'ayant pas de solution déterministe

Bounds for self-stabilization in unidirectional networks

A distributed algorithm is self-stabilizing if after faults and attacks hit the system and place it in some arbitrary global state, the systems recovers from this catastrophic situation without external intervention in finite time. Unidirectional networks preclude many common techniques in self-stabilization from being used, such as preserving local predicates. In this paper, we investigate the intrinsic complexity of achieving self-stabilization in unidirectional networks, and focus on the classical vertex coloring problem. When deterministic solutions are considered, we prove a lower bound of $n$ states per process (where $n$ is the network size) and a recovery time of at least $n(n-1)/2$ actions in total. We present a deterministic algorithm with matching upper bounds that performs in arbitrary graphs. When probabilistic solutions are considered, we observe that at least $\Delta + 1$ states per process and a recovery time of $\Omega(n)$ actions in total are required (where $\Delta$ denotes the maximal degree of the underlying simple undirected graph). We present a probabilistically self-stabilizing algorithm that uses $\mathtt{k}$ states per process, where $\mathtt{k}$ is a parameter of the algorithm. When $\mathtt{k}=\Delta+1$, the algorithm recovers in expected $O(\Delta n)$ actions. When $\mathtt{k}$ may grow arbitrarily, the algorithm recovers in expected O(n) actions in total. Thus, our algorithm can be made optimal with respect to space or time complexity

Concurrence et allocation de ressources locales instantanément stabilisante

International audienceCet article est un résumé de (Altisen et al., 2015) où nous étudions la notion de concurrence dans les problèmes d'allocation de ressources. Nous proposons des propriétés générales permettant d'exprimer la qualité de concurrence d'une solution à un problème d'allocation de ressources et établissons quelle qualité de concurrence peut être atteinte par un algorithme résolvant le problème d'allocation de ressources locales. Enfin, nous proposons un algorithme d'allocation de ressources locales instantanément stabilisant qui réalise cette qualité de concurrence

Snap-Stabilizing Committee Coordination

International audienceIn the committee coordination problem, a committee consists of a set of professors and committee meetingsare synchronized, so that each professor participates in at most one committee meeting at a time. Inthis paper, we propose two snap-stabilizing distributed algorithms for the committee coordination. Snapstabilizationis a versatile property which requires a distributed algorithm to efficiently tolerate transientfaults. Indeed, after a finite number of such faults, a snap-stabilizing algorithm immediately operates correctly,without any external intervention. We design snap-stabilizing committee coordination algorithmsenriched with some desirable properties related to concurrency, (weak) fairness, and a stronger synchronizationmechanism called 2-Phase Discussion. In our setting, all processes are identical and each processhas a unique identifier. The existing work in the literature has shown that (1) in general, fairness cannotbe achieved in committee coordination, and (2) it becomes feasible if each professor waits for meetingsinfinitely often. Nevertheless, we show that even under this latter assumption, it is impossible to implementa fair solution that allows maximal concurrency. Hence, we propose two orthogonal snap-stabilizingalgorithms, each satisfying 2-phase discussion, and either maximal concurrency or fairness. The algorithmthat implements fairness requires that every professor waits for meetings infinitely often. Moreover, forthis algorithm, we introduce and evaluate a new efficiency criterion called the degree of fair concurrency.This criterion shows that even if it does not satisfy maximal concurrency, our snap-stabilizing fair algorithmstill allows a high level of concurrency

Self-stabilizing K-out-of-L exclusion on tree network

In this paper, we address the problem of K-out-of-L exclusion, a generalization of the mutual exclusion problem, in which there are $\ell$ units of a shared resource, and any process can request up to $\mathtt k$ units ($1\leq\mathtt k\leq\ell$). We propose the first deterministic self-stabilizing distributed K-out-of-L exclusion protocol in message-passing systems for asynchronous oriented tree networks which assumes bounded local memory for each process.Comment: 15 page

Communication Efficiency in Self-stabilizing Silent Protocols

Self-stabilization is a general paradigm to provide forward recovery capabilities to distributed systems and networks. Intuitively, a protocol is self-stabilizing if it is able to recover without external intervention from any catastrophic transient failure. In this paper, our focus is to lower the communication complexity of self-stabilizing protocols \emph{below} the need of checking every neighbor forever. In more details, the contribution of the paper is threefold: (i) We provide new complexity measures for communication efficiency of self-stabilizing protocols, especially in the stabilized phase or when there are no faults, (ii) On the negative side, we show that for non-trivial problems such as coloring, maximal matching, and maximal independent set, it is impossible to get (deterministic or probabilistic) self-stabilizing solutions where every participant communicates with less than every neighbor in the stabilized phase, and (iii) On the positive side, we present protocols for coloring, maximal matching, and maximal independent set such that a fraction of the participants communicates with exactly one neighbor in the stabilized phase

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