A tight runtime bound for synchronous gathering of autonomous robots with limited visibility

Degener, Bastian; Kempkes, Barbara; Langner, Tobias; Heide, Friedhelm Meyer auf der; Pietrzyk, Peter; Wattenhofer, Roger

doi:10.1145/1989493.1989515

Cited by 74 publications

(40 citation statements)

References 27 publications

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“…In particular, three models are commonly used: Fsync, Ssync, and Async; the fully synchronous model Fsync is the strongest, the asynchronous model Async is the weakest, and the semisynchronous model Ssync lies in between. In the synchronous models (Fsync and Ssync), the cycles of all robots are fully synchronized: the sensors that become active do so all at the same time and each operation of the life cycle is performed by all robots simultaneously [1,6,11,13,19,20,21,29,41,52]. In the asynchronous model (Async), there is no global clock, and the robots do not have a common notion of time; furthermore, the duration of each activity (or inactivity) is finite but unpredictable [15,26,27,36,46].…”

Section: Settingmentioning

confidence: 99%

“…An interesting fundamental research question is the definition of cost measures and their use in the analysis of the complexity of the solution protocols. A step in this direction has been taken recently, analyzing the number of rounds for the (simpler) Converge problem in the case of synchronous robots [19]. of l and l , respectively, at time t. Recall that, by Property 10, when executing movePairwiseCautiously(l , l , c) at time t, l (resp., l ) will perform a nonnull movement only if |N (t)| ≥ |N (t)| (resp., |N (t)| ≥ |N (t)|).…”

Section: Correctness Of Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Distributed Computing by Mobile Robots: Gathering

Cieliebak¹,

Flocchini²,

Prencipe³

et al. 2012

SIAM J. Comput.

199

147

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Abstract. Consider a set of n > 2 identical mobile computational entities in the plane, called robots, operating in Look-Compute-Move cycles, without any means of direct communication. The Gathering Problem is the primitive task of all entities gathering in finite time at a point not fixed in advance, without any external control. The problem has been extensively studied in the literature under a variety of strong assumptions (e.g., synchronicity of the cycles, instantaneous movements, complete memory of the past, common coordinate system, etc.). In this paper we consider the setting without those assumptions, that is, when the entities are oblivious (i.e., they do not remember results and observations from previous cycles), disoriented (i.e., have no common coordinate system), and fully asynchronous (i.e., no assumptions exist on timing of cycles and activities within a cycle). The existing algorithmic contributions for such robots are limited to solutions for n ≤ 4 or for restricted sets of initial configurations of the robots; the question of whether such weak robots could deterministically gather has remained open. In this paper, we prove that indeed the Gathering Problem is solvable, for any n > 2 and any initial configuration, even under such restrictive conditions.

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Section: Settingmentioning

confidence: 99%

Section: Correctness Of Algorithmmentioning

confidence: 99%

Distributed Computing by Mobile Robots: Gathering

Cieliebak¹,

Flocchini²,

Prencipe³

et al. 2012

SIAM J. Comput.

199

147

View full text Add to dashboard Cite

show abstract

“…A different goal, but with a similar model for the robots and their environment, is pursued by Degener et al in [5]. Instead of forming a circle, the robots gather at a single point on the plane in O(n 2 ) rounds with n being the number of robots.…”

Section: B Related Workmentioning

confidence: 99%

Self-organizing Particle Systems

Drees

Hüllmann

Koutsopoulos

et al. 2012

2012 IEEE 26th International Parallel and Distributed Processing Symposium

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Abstract-Nanoparticles are getting more and more in the focus of the scientific community since the potential for the development of very small particles interacting with each other and completing medical and other tasks is getting bigger year by year. In this work we introduce a distributed local algorithm for arranging a set of nanoparticles on the discrete plane into specific geometric shapes, for instance a rectangle. The concept of a particle we use can be seen as a simple mobile robot with the following restrictions: it can only view the state of robots it is physically connected to, is anonymous, has only a constant size memory, can only move by using other particles as an anchor point on which it pulls itself alongside, and it operates in Look-ComputeMove cycles. The main result of this work is the presentation of a random distributed local algorithm which transforms any given connected set of particles into a particular geometric shape. As an example we provide a version of this algorithm for forming a rectangle with an arbitrary predefined aspect ratio. To the best of our knowledge this is the first work that considers arrangement problems for these types of robots.

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“…We study one of the most fundamental problems of self-organization of mobile entities, known in the literature as the gathering problem (see e.g., [8,10,14] and references therein). In particular, we consider oblivious robots initially located at different nodes of an anonymous ring that have to gather at a common node and remain in there.…”

Section: Introductionmentioning

confidence: 99%

“…The problem of let meet mobile entities on graphs [2,11,20] or open spaces [5,10,22] has been extensively studied in the last decades. When only two robots are involved, the problem is referred to as the rendezvous problem [1,4,6,11,23].…”

Section: Introductionmentioning

confidence: 99%

How to Gather Asynchronous Oblivious Robots on Anonymous Rings

D’Angelo

Stefano

Navarra

2012

Lecture Notes in Computer Science

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Abstract. A set of robots arbitrarily placed on different nodes of an anonymous ring have to meet at one common node and remain in there. This problem is known in the literature as the gathering. Anonymous and oblivious robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), decides whether to stay idle or to move to one of its neighbors (Compute), and in the latter case makes the computed move instantaneously (Move). Cycles are asynchronous among robots. Moreover, each robot is empowered by the so called multiplicity detection capability, that is, it is able to detect during its Look operation whether a node is empty, or occupied by one robot, or occupied by an undefined number of robots greater than one. The described problem has been extensively studied during the last years. However, the known solutions work only for specific initial configurations and leave some open cases. In this paper, we provide an algorithm which solves the general problem, and is able to detect all the ungatherable configurations. It is worth noting that our new algorithm makes use of a unified and general strategy for any initial configuration, even those left open by previous works.

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A tight runtime bound for synchronous gathering of autonomous robots with limited visibility

Cited by 74 publications

References 27 publications

Distributed Computing by Mobile Robots: Gathering

Distributed Computing by Mobile Robots: Gathering

Self-organizing Particle Systems

How to Gather Asynchronous Oblivious Robots on Anonymous Rings

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