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

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

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

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

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

Imagining Earth: Concepts of Wholeness in Cultural Constructions of Our Home Planet

While concepts of Earth have a rich tradition, more recent examples show a distinct quality: Though ideas of wholeness might still be related to mythical, religious, or utopian visions of the past, "Earth" itself has become available as a whole. This raises several questions: How are the notions of one Earth or our Planet imagined and distributed? What is the role of cultural imagination and practices of signification in the imagination of "the Earth"? Which theoretical models can be used or need to be developed to describe processes of imagining Planet Earth? This collection invites a wide range of perspectives from different fields of the Humanities to explore the means of imagining Earth

Imagining Earth

While concepts of Earth have a rich tradition, more recent examples show a distinct quality: Though ideas of wholeness might still be related to mythical, religious, or utopian visions of the past, ''Earth'' itself has become available as a whole. This raises several questions: How are the notions of one Earth or our Planet imagined and distributed? What is the role of cultural imagination and practices of signification in the imagination of ''the Earth''? Which theoretical models can be used or need to be developed to describe processes of imagining Planet Earth? This collection invites a wide range of perspectives from different fields of the Humanities to explore the means of imagining Earth