Nicolas Nisse, Alfredo Navarra, Gianlorenzo D'Angelo, Dipartimento di Matematica e Informatica [Perugia] (DMI), Università degli Studi di Perugia (UNIPG), Combinatorics, Optimization and Algorithms for Telecommunications (COATI), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-COMmunications, Réseaux, systèmes Embarqués et Distribués (Laboratoire I3S - COMRED), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Inria Chile, Universidad Diego Portales [Santiago] (UDP)-Universidad de la frontera [Chile]-Universidad de Concepción [Chile]-Pontificia Universidad Católica de Chile (UC)-Institut National de Recherche en Informatique et en Automatique (Inria)-Pontificia Universidad Católica de Valparaíso (PUCV)-Universidad Adolfo Ibáñez [Santiago]-Universidad de Valparaiso [Chile]-Universidad Tecnica Federico Santa Maria [Valparaiso] (UTFSM), Mainak Chatterjee, Jian-Nong Cao, Kishore Kothapalli, Sergio Rajsbaum, Universidad de Valparaiso [Chile]-Universidad Tecnica Federico Santa Maria [Valparaiso] (UTFSM)-Universidad Adolfo Ibáñez [Santiago]-Pontificia Universidad Católica de Valparaíso (PUCV)-Institut National de Recherche en Informatique et en Automatique (Inria)-Pontificia Universidad Católica de Chile (UC)-Universidad de Concepción [Chile]-Universidad de la frontera [Chile]-Universidad Diego Portales [Santiago] (UDP), Università degli Studi di Perugia = University of Perugia (UNIPG), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and Universidad Diego Portales [Santiago] (UDP)-Universidad de la frontera [Chile]-Pontificia Universidad Católica de Chile (UC)-Institut National de Recherche en Informatique et en Automatique (Inria)-Pontificia Universidad Católica de Valparaíso (PUCV)-Universidad Adolfo Ibáñez [Santiago]-Universidad de Valparaiso [Chile]-Universidad Tecnica Federico Santa Maria [Valparaiso] (UTFSM)-Universidad de Concepción - University of Concepcion [Chile]
International audience; Consider a set of mobile robots with minimal capabilities placed over distinct nodes of a discrete anonymous ring. Asynchronously, each robot takes a snapshot of the ring, determining which nodes are either occupied by robots or empty. Based on the observed configuration, it decides whether to move to one of its adjacent nodes or not. In the first case, it performs the computed move, eventually. The computation also depends on the required task. In this paper, we solve both the well-known Gathering and Exclusive Searching tasks. In the former problem, all robots must simultaneously occupy the same node, eventually. In the latter problem, the aim is to clear all edges of the graph. An edge is cleared if it is traversed by a robot or if both its endpoints are occupied. We consider the exclusive searching where it must be ensured that two robots never occupy the same node. Moreover, since the robots are oblivious, the clearing is perpetual, i.e., the ring is cleared infinitely often. In the literature, most contributions are restricted to a subset of initial configurations. Here, we design two different algorithms and provide a characterization of the initial configurations that permit the resolution of the problems under minimal assumptions.