137 research outputs found

    Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots

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    We consider a team of kk 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 Θ(log⁥n)\Theta(\log n) robots are necessary and sufficient to solve the problem with kk deterministic robots, provided that kk and nn 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

    Optimal deterministic ring exploration with oblivious asynchronous robots

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    We consider the problem of exploring an anonymous unoriented ring of size nn by kk identical, oblivious, asynchronous mobile robots, that are unable to communicate, yet have the ability to sense their environment and take decisions based on their local view. Previous works in this weak scenario prove that kk must not divide nn for a deterministic solution to exist. Also, it is known that the minimum number of robots (either deterministic or probabilistic) to explore a ring of size nn is 4. An upper bound of 17 robots holds in the deterministic case while 4 probabilistic robots are sufficient. In this paper, we close the complexity gap in the deterministic setting, by proving that no deterministic exploration is feasible with less than five robots whenever the size of the ring is even, and that five robots are sufficient for any nn that is coprime with five. Our protocol completes exploration in O(n) robot moves, which is also optimal

    Optimal Torus Exploration by Oblivious Robots

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    International audienceWe consider autonomous robots that are endowed with motion actuators and visibility sensors. The robots we consider are weak, i.e., they are anonymous, uniform, unable to explicitly communicate, and oblivious (they do not remember any of their past actions). In this paper, we propose an optimal (w.r.t. the number of robots) solution for the terminating exploration of a torus-shaped network by a team of kk such robots. In more details, we first show that it is impossible to explore a simple torus of arbitrary size with (strictly) less than four robots, even if the algorithm is probabilistic. If the algorithm is required to be deterministic, four robots are also insufficient. This negative result implies that the only way to obtain an optimal algorithm (w.r.t. the number of robots participating to the algorithm) is to make use of probabilities. Then, we propose a probabilistic algorithm that uses four robots to explore all simple tori of size ℓ×L\ell \times L, where 7≀ℓ≀L7 \leq \ell \leq L. Hence, in such tori, four robots are necessary and sufficient to solve the (probabilistic) terminating exploration. As a torus can be seen as a 2-dimensional ring, our result shows, perhaps surprisingly, that increasing the number of possible symmetries in the network (due to increasing dimensions) does not come at an extra cost w.r.t. the number of robots that are necessary to solve the problem

    Optimal torus exploration by oblivious robots

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    International audienceWe deal with a team of autonomous robots that are endowed with motion actuators and visibility sensors. Those robots are weak and evolve in a discrete environment. By weak, we mean that they are anonymous, uniform, unable to explicitly communicate, and oblivious. We first show that it is impossible to solve the terminating exploration of a simple torus of arbitrary size with less than 4 or 5 such robots, respectively depending on whether the algorithm is probabilistic or deterministic. Next, we propose in the SSYNC model a probabilistic solution for the terminating exploration of torus-shaped networks of size ℓ×L, where 7≀ℓ≀L, by a team of 4 such weak robots. So, this algorithm is optimal w.r.t. the number of robots

    Deterministic Symmetry Breaking in Ring Networks

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    We study a distributed coordination mechanism for uniform agents located on a circle. The agents perform their actions in synchronised rounds. At the beginning of each round an agent chooses the direction of its movement from clockwise, anticlockwise, or idle, and moves at unit speed during this round. Agents are not allowed to overpass, i.e., when an agent collides with another it instantly starts moving with the same speed in the opposite direction (without exchanging any information with the other agent). However, at the end of each round each agent has access to limited information regarding its trajectory of movement during this round. We assume that nn mobile agents are initially located on a circle unit circumference at arbitrary but distinct positions unknown to other agents. The agents are equipped with unique identifiers from a fixed range. The {\em location discovery} task to be performed by each agent is to determine the initial position of every other agent. Our main result states that, if the only available information about movement in a round is limited to %information about distance between the initial and the final position, then there is a superlinear lower bound on time needed to solve the location discovery problem. Interestingly, this result corresponds to a combinatorial symmetry breaking problem, which might be of independent interest. If, on the other hand, an agent has access to the distance to its first collision with another agent in a round, we design an asymptotically efficient and close to optimal solution for the location discovery problem.Comment: Conference version accepted to ICDCS 201

    Uniform multi-agent deployment on a ring

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    AbstractWe consider two variants of the task of spreading a swarm of agents uniformly on a ring graph. Ant-like oblivious agents having limited capabilities are considered. The agents are assumed to have little memory, they all execute the same algorithm and no direct communication is allowed between them. Furthermore, the agents do not possess any global information. In particular, the size of the ring (n) and the number of agents in the swarm (k) are unknown to them. The agents are assumed to operate on an unweighted ring graph. Every agent can measure the distance to his two neighbors on the ring, up to a limited range of V edges.The first task considered, is dynamical (i.e. in motion) uniform deployment on the ring. We show that if either the ring is unoriented, or the visibility range is less than ⌊n/k⌋, this is an impossible mission for the agents. Then, for an oriented ring and V≄⌈n/k⌉, we propose an algorithm which achieves the deployment task in optimal time. The second task discussed, called quiescent spread, requires the agents to spread uniformly over the ring and stop moving. We prove that under our model, in which every agent can measure the distance only to his two neighbors, this task is impossible. Subsequently, we propose an algorithm which achieves quiescent but only almost uniform spread.The algorithms we present are scalable and robust. In case the environment (the size of the ring) or the number of agents changes during the run, the swarm adapts and re-deploys without requiring any outside interference

    Ring Exploration with Oblivious Myopic Robots

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    The exploration problem in the discrete universe, using identical oblivious asynchronous robots without direct communication, has been well investigated. These robots have sensors that allow them to see their environment and move accordingly. However, the previous work on this problem assume that robots have an unlimited visibility, that is, they can see the position of all the other robots. In this paper, we consider deterministic exploration in an anonymous, unoriented ring using asynchronous, oblivious, and myopic robots. By myopic, we mean that the robots have only a limited visibility. We study the computational limits imposed by such robots and we show that under some conditions the exploration problem can still be solved. We study the cases where the robots visibility is limited to 1, 2, and 3 neighboring nodes, respectively.Comment: (2012

    A Certified Universal Gathering Algorithm for Oblivious Mobile Robots

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    We present a new algorithm for the problem of universal gathering mobile oblivious robots (that is, starting from any initial configuration that is not bivalent, using any number of robots, the robots reach in a finite number of steps the same position, not known beforehand) without relying on a common chirality. We give very strong guaranties on the correctness of our algorithm by proving formally that it is correct, using the COQ proof assistant. To our knowledge, this is the first certified positive (and constructive) result in the context of oblivious mobile robots. It demonstrates both the effectiveness of the approach to obtain new algorithms that are truly generic, and its managability since the amount of developped code remains human readable

    Terminating Exploration Of A Grid By An Optimal Number Of Asynchronous Oblivious Robots

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    International audienceWe consider swarms of asynchronous oblivious robots evolving into an anonymous grid-shaped network. In this context, we investigate optimal (w.r.t. the number of robots) deterministic solutions for the terminating exploration problem. We first show lower bounds in the semi-synchronous model. Precisely, we show that at least three robots are required to explore any grid of at least three nodes, even in the probabilistic case. Then, we show that at least four (resp. five) robots are necessary to deterministically explore a (2,2)-Grid (resp. a (3,3)-Grid). We then propose deterministic algorithms in the asynchronous model. This latter being strictly weakest than the semi-synchronous model, all the aforementioned bounds still hold in that context. Our algorithms actually exhibit the optimal number of robots that is necessary to explore a given grid. Overall, our results show that except in two particular cases, three robots are necessary and sufficient to deterministically explore a grid of at least three nodes and then terminate. The optimal number of robots for the two remaining cases is four for the (2,2)-Grid and five for the (3,3)-Grid, respectively
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