Gracefully Degrading Gathering in Dynamic Rings

Gracefully degrading algorithms [Biely \etal, TCS 2018] are designed to circumvent impossibility results in dynamic systems by adapting themselves to the dynamics. Indeed, such an algorithm solves a given problem under some dynamics and, moreover, guarantees that a weaker (but related) problem is solved under a higher dynamics under which the original problem is impossible to solve. The underlying intuition is to solve the problem whenever possible but to provide some kind of quality of service if the dynamics become (unpredictably) higher.In this paper, we apply for the first time this approach to robot networks. We focus on the fundamental problem of gathering a squad of autonomous robots on an unknown location of a dynamic ring. In this goal, we introduce a set of weaker variants of this problem. Motivated by a set of impossibility results related to the dynamics of the ring, we propose a gracefully degrading gathering algorithm

Asynchronous approach in the plane: A deterministic polynomial algorithm

In this paper we study the task of approach of two mobile agents having the same limited range of vision and moving asynchronously in the plane. This task consists in getting them in finite time within each other's range of vision. The agents execute the same deterministic algorithm and are assumed to have a compass showing the cardinal directions as well as a unit measure. On the other hand, they do not share any global coordinates system (like GPS), cannot communicate and have distinct labels. Each agent knows its label but does not know the label of the other agent or the initial position of the other agent relative to its own. The route of an agent is a sequence of segments that are subsequently traversed in order to achieve approach. For each agent, the computation of its route depends only on its algorithm and its label. An adversary chooses the initial positions of both agents in the plane and controls the way each of them moves along every segment of the routes, in particular by arbitrarily varying the speeds of the agents. A deterministic approach algorithm is a deterministic algorithm that always allows two agents with any distinct labels to solve the task of approach regardless of the choices and the behavior of the adversary. The cost of a complete execution of an approach algorithm is the length of both parts of route travelled by the agents until approach is completed. Let $\Delta$ and $l$ be the initial distance separating the agents and the length of the shortest label, respectively. Assuming that $\Delta$ and $l$ are unknown to both agents, does there exist a deterministic approach algorithm always working at a cost that is polynomial in $\Delta$ and $l$? In this paper, we provide a positive answer to the above question by designing such an algorithm

Asynchronous Approach in the Plane: A Deterministic Polynomial Algorithm

In this paper we study the task of approach of two mobile agents having the same limited range of vision and moving asynchronously in the plane. This task consists in getting them in finite time within each other\u27s range of vision. The agents execute the same deterministic algorithm and are assumed to have a compass showing the cardinal directions as well as a unit measure. On the other hand, they do not share any global coordinates system (like GPS), cannot communicate and have distinct labels. Each agent knows its label but does not know the label of the other agent or the initial position of the other agent relative to its own. The route of an agent is a sequence of segments that are subsequently traversed in order to achieve approach. For each agent, the computation of its route depends only on its algorithm and its label. An adversary chooses the initial positions of both agents in the plane and controls the way each of them moves along every segment of the routes, in particular by arbitrarily varying the speeds of the agents. Roughly speaking, the goal of the adversary is to prevent the agents from solving the task, or at least to ensure that the agents have covered as much distance as possible before seeing each other. A deterministic approach algorithm is a deterministic algorithm that always allows two agents with any distinct labels to solve the task of approach regardless of the choices and the behavior of the adversary. The cost of a complete execution of an approach algorithm is the length of both parts of route travelled by the agents until approach is completed. Let Delta and l be the initial distance separating the agents and the length of (the binary representation of) the shortest label, respectively. Assuming that Delta and l are unknown to both agents, does there exist a deterministic approach algorithm whose cost is polynomial in Delta and l? Actually the problem of approach in the plane reduces to the network problem of rendezvous in an infinite oriented grid, which consists in ensuring that both agents end up meeting at the same time at a node or on an edge of the grid. By designing such a rendezvous algorithm with appropriate properties, as we do in this paper, we provide a positive answer to the above question. Our result turns out to be an important step forward from a computational point of view, as the other algorithms allowing to solve the same problem either have an exponential cost in the initial separating distance and in the labels of the agents, or require each agent to know its starting position in a global system of coordinates, or only work under a much less powerful adversary

Gracefully Degrading Gathering in Dynamic Rings

Gracefully degrading algorithms [Biely \etal, TCS 2018] are designed to circumvent impossibility results in dynamic systems by adapting themselves to the dynamics. Indeed, such an algorithm solves a given problem under some dynamics and, moreover, guarantees that a weaker (but related) problem is solved under a higher dynamics under which the original problem is impossible to solve. The underlying intuition is to solve the problem whenever possible but to provide some kind of quality of service if the dynamics become (unpredictably) higher.In this paper, we apply for the first time this approach to robot networks. We focus on the fundamental problem of gathering a squad of autonomous robots on an unknown location of a dynamic ring. In this goal, we introduce a set of weaker variants of this problem. Motivated by a set of impossibility results related to the dynamics of the ring, we propose a gracefully degrading gathering algorithm

Computability of Perpetual Exploration in Highly Dynamic Rings

We consider systems made of autonomous mobile robots evolving in highly dynamic discrete environment i.e., graphs where edges may appear and disappear unpredictably without any recurrence, stability, nor periodicity assumption. Robots are uniform (they execute the same algorithm), they are anonymous (they are devoid of any observable ID), they have no means allowing them to communicate together, they share no common sense of direction, and they have no global knowledge related to the size of the environment. However, each of them is endowed with persistent memory and is able to detect whether it stands alone at its current location. A highly dynamic environment is modeled by a graph such that its topology keeps continuously changing over time. In this paper, we consider only dynamic graphs in which nodes are anonymous, each of them is infinitely often reachable from any other one, and such that its underlying graph (i.e., the static graph made of the same set of nodes and that includes all edges that are present at least once over time) forms a ring of arbitrary size. In this context, we consider the fundamental problem of perpetual exploration: each node is required to be infinitely often visited by a robot. This paper analyzes the computability of this problem in (fully) synchronous settings, i.e., we study the deterministic solvability of the problem with respect to the number of robots. We provide three algorithms and two impossibility results that characterize, for any ring size, the necessary and sufficient number of robots to perform perpetual exploration of highly dynamic rings

Gracefully Degrading Gathering in Dynamic Rings

Gracefully degrading algorithms [Biely \etal, TCS 2018] are designed to circumvent impossibility results in dynamic systems by adapting themselves to the dynamics. Indeed, such an algorithm solves a given problem under some dynamics and, moreover, guarantees that a weaker (but related) problem is solved under a higher dynamics under which the original problem is impossible to solve. The underlying intuition is to solve the problem whenever possible but to provide some kind of quality of service if the dynamics become (unpredictably) higher.In this paper, we apply for the first time this approach to robot networks. We focus on the fundamental problem of gathering a squad of autonomous robots on an unknown location of a dynamic ring. In this goal, we introduce a set of weaker variants of this problem. Motivated by a set of impossibility results related to the dynamics of the ring, we propose a gracefully degrading gathering algorithm

Quel est le nombre optimal de robots pour explorer un anneau hautement dynamique ?

International audienceDans cet article, nous nous intéressons à la coordination algorithmique d'une cohorte de robots mobiles. Ces robots sont autonomes, uniformes, anonymes, capables de percevoir leur environnement, mais pas de communiquer. Ils évoluent de manière synchrone dans un environnement fini et discret représenté par un graphe. Nous supposons que cet environnement est un anneau hautement dynamique, c'est-à-dire un anneau dont les arêtes peuvent apparaître et disparaître de manière imprévisible sans aucune hypothèse de récurrence, de stabilité ou de périodicité à travers le temps mais avec une hypothèse de connexité temporelle minimale à la résolution du problème. Nous nous intéressons en particulier au problème de l'exploration perpétuelle de ce type de graphe, problème dans lequel chaque nœud de l'anneau doit être infiniment souvent visité par un robot. Notre contribution est la caractérisation exhaustive du nombre de robots nécessaires et suffisants pour résoudre ce problème en fonction de la taille de l'anneau

Computability of Perpetual Exploration in Highly Dynamic Rings

International audienceWe consider systems made of autonomous mobile robots evolving in highly dynamic discrete environment, i.e., graphs where edges may appear and disappear unpredictably without any recurrence, stability, nor periodicity assumption. Robots are uniform (they execute the same algorithm), they are anonymous (they are devoid of any observable ID), they have no means allowing them to communicate together, they share no common sense of direction, and they have no global knowledge related to the size of the environment. However, each of them is endowed with persistent memory and is able to detect whether it stands alone at its current location. A highly dynamic environment is modeled by a graph such that its topology keeps continuously changing over time. In this paper, we consider only dynamic graphs in which nodes are anonymous, each of them is infinitely often reachable from any other one, and such that its underlying graph (i.e., the static graph made of the same set of nodes and that includes all edges that are present at least once over time) forms a ring of arbitrary size. In this context, we consider the fundamental problem of perpetual exploration: each node is required to be infinitely often visited by a robot.This paper analyses the computability of this problem in (fully) synchronous settings, i.e., we study the deterministic solvability of the problem with respect to the number of robots. We provide three algorithms and two impossibility results that characterize, for any ring size, the necessary and sufficient number of robots to perform perpetual exploration of highly dynamic rings

Approche asynchrone dans le plan : un algorithme déterministe polynomial

International audienceNous étudions la tâche de l'approche entre deux agents mobiles ayant la même portée de vision limitée et se déplaçant de façon asynchrone dans le plan. En partant de positions initiales quelconques, cette tâche consiste à les amener au moyen d'un algorithme déterministe à portée de vision l'un de l'autre en un temps fini. Ils sont autonomes et ne peuvent pas communiquer entre eux. Ils disposent cependant d'identifiants distincts et d'une boussole leur indiquant les points cardinaux. Chaque agent ne connaît que son identifiant. En particulier, il ignore l'identifiant et la position initiale de l'autre agent. Un adversaire choisit les identifiants et les positions initiales des deux agents dans le plan et modifie à volonté la vitesse à laquelle chacun se déplace. Le coût d'une exécution complète d'un algorithme pour cette tâche est la somme des distances parcourues par les deux agents jusqu'à accomplir l'approche. Dans ces conditions, certains algorithmes déterministes résolvent cette tâche avec un coût exponentiel en fonction de la distance initiale ∆ séparant les deux robots et de la longueur des identifiants. D'autres nécessitent que chaque agent connaisse sa position de départ dans un système de coordonnées commun ; d'autres encore fonctionnent avec un adversaire plus faible. Ce papier présente un algorithme déterministe pour la tâche de l'approche dont le coût est polynomial en fonction de ∆ et de la longueur (de la représentation binaire) du plus petit identifiant

Elastic Management of Byzantine Faults

International audienceTolerating byzantine faults on a large scale is a challenge: in particular, Desktop Grid environments sustain large numbers of faults that range from crashes to byzantine faults. Solutions in the literature that address byzantine failures are costly and none of them scales to really large numbers of nodes. This paper proposes to distribute task scheduling on trusted nodes in a Cloud network and to have these nodes assess the reliability of worker nodes by means of a reputation system. The resulting architecture is built for scalability and adapts costs to the workload associated with client requests