Optimal Probabilistic Ring Exploration by Semi-synchronous Oblivious Robots

Devismes, Stéphane; Petit, Franck; Tixeuil, Sébastien

doi:10.1007/978-3-642-11476-2_16

Cited by 31 publications

(33 citation statements)

References 15 publications

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“…Two types of exploration tasks have been well studied: perpetual exploration requires robots to visit nodes so that every node is visited infinitely many times by a robot, and terminating exploration requires robots to terminate after every node is visited by a robot at least once. For example, perpetual exploration has been studied for rings [1] and grids [2], and terminating exploration has been studied for rings [14,16], trees [15], grids [12], tori [13], and arbitrary networks [3].…”

Section: Background and Motivationmentioning

confidence: 99%

Ring Exploration with Myopic Luminous Robots

Ooshita

Tixeuil

2018

Lecture Notes in Computer Science

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We investigate exploration algorithms for autonomous mobile robots evolving in uniform ring-shaped networks. Different from the usual Look-Compute-Move (LCM) model, we consider two characteristics: myopia and luminosity. Myopia means each robot has a limited visibility. We consider the weakest assumption for myopia: each robot can only observe its neighboring nodes. Luminosity means each robot maintains a non-volatile visible light. We consider the weakest assumption for luminosity: each robot can use only two colors for its light. The main interest of this paper is to clarify the impact of luminosity on exploration with myopic robots.As a main contribution, we prove that 1) in the fully synchronous model, two and three robots are necessary and sufficient to achieve perpetual and terminating exploration, respectively, and 2) in the semi-synchronous and asynchronous models, three and four robots are necessary and sufficient to achieve perpetual and terminating exploration, respectively. These results clarify the power of lights for myopic robots since, without lights, five robots are necessary and sufficient to achieve terminating exploration in the fully synchronous model, and no terminating exploration algorithm exists in the semi-synchronous and asynchronous models.We also show that, in the fully synchronous model (resp., the semi-synchronous and asynchronous models), the proposed perpetual exploration algorithm is universal, that is, the algorithm solves perpetual exploration from any solvable initial configuration with two (resp., three) robots and two colors. On the other hand, we show that, in the fully synchronous model (resp., the semi-synchronous and asynchronous models), no universal algorithm exists for terminating exploration, that is, no algorithm may solve terminating exploration from any solvable initial configuration with three (resp., four) robots and two colors.

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Section: Background and Motivationmentioning

confidence: 99%

Ring Exploration with Myopic Luminous Robots

Ooshita

Tixeuil

2018

Lecture Notes in Computer Science

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“…To fit various applications and environments, numerous variants of exploration have been studied in the literature, for instance, terminating exploration -the robots stop moving after completion of the exploration of the whole graph [8,9,13]-, exclusive perpetual exploration -every node is visited infinitely often, but no two robots collide at the same node [1,2]-, exploration with return -each robot comes back to its initial location once the exploration is completed [11] -, etc.. Clearly, some of these variants may be mixed (e.g., exclusive perpetual exploration vs. non exclusive terminating exploration) and either weakened or strengthened (weak perpetual exploration -every node is visited infinitely often by at least one robot [3]-vs. strong perpetual exploration -every node is visited infinitely often by each robot-, etc.). Note that all these instances of exploration are different problems in the sense that, in most of the cases, solutions for any given instance cannot be used to solve another instance.…”

Section: Introductionmentioning

confidence: 99%

Computability of Perpetual Exploration in Highly Dynamic Rings

Bournat¹,

Dubois²,

Petit³

2017

2017 IEEE 37th International Conference on Distributed Computing Systems (ICDCS)

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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.

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“…Indeed, since the network's port numbers may not be unique, it may be impossible for an algorithm to unambiguously indicate where each robot has to move. This model, introduced by Klasing, Markou, and Pelc [22] as an extension of the model of oblivious robots in continuous spaces (e.g., [14]), has been extensively employed and investigated, focusing on basic problems in specific classes of graphs under different schedulers: gathering and scattering (e.g., [4,5,6,7,10,16,17,19,21,22,25,26]), and exploration and traversal (e.g., [1,2,3,8,9,11,12,13,23,24]). Note that, with the exception of [3], the literature assumes unlabelled edges.…”

Section: Introductionmentioning

confidence: 99%

Universal Systems of Oblivious Mobile Robots

Flocchini

Santoro

Viglietta

et al. 2016

Structural Information and Communication Complexity

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An oblivious mobile robot is a stateless computational entity located in a spatial universe, capable of moving in that universe. When activated, the robot observes the universe and the location of the other robots, chooses a destination, and moves there. The computation of the destination is made by executing an algorithm, the same for all robots, whose sole input is the current observation. No memory of all these actions is retained after the move. When the spatial universe is a graph, distributed computations by oblivious mobile robots have been intensively studied focusing on the conditions for feasibility of basic problems (e.g., gathering, exploration) in specific classes of graphs under different schedulers. In this paper, we embark on a different, more general, type of investigation.With their movements from vertices to neighboring vertices, the robots make the system transition from one configuration to another. Thus the execution of an algorithm from a given configuration defines in a natural way the computation of a discrete function by the system. Our research interest is to understand which functions are computed by which systems. In this paper we focus on identifying sets of systems that are universal, in the sense that they can collectively compute all finite functions. We are able to identify several such classes of fully synchronous systems. In particular, among other results, we prove the universality of the set of all graphs with at least one robot, of any set of graphs with at least two robots whose quotient graphs contain arbitrarily long paths, and of any set of graphs with at least three robots and arbitrarily large finite girths.We then focus on the minimum size that a network must have for the robots to be able to compute all functions on a given finite set. We are able to approximate the minimum size of such a network up to a factor that tends to 2 as n goes to infinity.The main technique we use in our investigation is the simulation between algorithms, which in turn defines domination between systems. If a system dominates another system, then it can compute at least as many functions. The other ingredient is constituted by path and ring networks, of which we give a thorough analysis. Indeed, in terms of implicit function computations, they are revealed to be fundamental topologies with important properties. Understanding these properties enables us to extend our results to larger classes of graphs, via simulation.

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Optimal Probabilistic Ring Exploration by Semi-synchronous Oblivious Robots

Cited by 31 publications

References 15 publications

Ring Exploration with Myopic Luminous Robots

Ring Exploration with Myopic Luminous Robots

Computability of Perpetual Exploration in Highly Dynamic Rings

Universal Systems of Oblivious Mobile Robots

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