Randomized Rendezvous Algorithms for Agents on a Ring with Different Speeds

Kranakis, Evangelos; Kriz̧anc, Danny; MacQuarrie, Fraser; Shende, Sunil

doi:10.1145/2684464.2684468

Cited by 7 publications

(2 citation statements)

References 32 publications

(27 reference statements)

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“…Other works [25,29] investigated Gathering on a circle in the continuous model, where robots observe and update their movement direction at every instant. However, the proposed solutions strongly rely on either randomness or different robot speeds, both of which are ways to break symmetry.…”

Section: Related Workmentioning

confidence: 99%

Gathering on a Circle with Limited Visibility by Anonymous Oblivious Robots

Luna¹,

Uehara²,

Viglietta³

et al. 2020

Preprint

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A swarm of anonymous oblivious mobile robots, operating in deterministic Look-Compute-Move cycles, is confined within a circular track. All robots agree on the clockwise direction (chirality), they are activated by an adversarial semi-synchronous scheduler (SSYNCH), and an active robot always reaches the destination point it computes (rigidity). Robots have limited visibility: each robot can see only the points on the circle that have an angular distance strictly smaller than a constant ϑ from the robot's current location, where 0 < ϑ ≤ π (angles are expressed in radians).We study the Gathering problem for such a swarm of robots: that is, all robots are initially in distinct locations on the circle, and their task is to reach the same point on the circle in a finite number of turns, regardless of the way they are activated by the scheduler. Note that, due to the anonymity of the robots, this task is impossible if the initial configuration is rotationally symmetric; hence, we have to make the assumption that the initial configuration be rotationally asymmetric.We prove that, if ϑ = π (i.e., each robot can see the entire circle except its antipodal point), there is a distributed algorithm that solves the Gathering problem for swarms of any size. By contrast, we also prove that, if ϑ ≤ π/2, no distributed algorithm solves the Gathering problem, regardless of the size of the swarm, even under the assumption that the initial configuration is rotationally asymmetric and the visibility graph of the robots is connected.The latter impossibility result relies on a probabilistic technique based on random perturbations, which is novel in the context of anonymous mobile robots. Such a technique is of independent interest, and immediately applies to other Pattern-Formation problems.

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Section: Related Workmentioning

confidence: 99%

Gathering on a Circle with Limited Visibility by Anonymous Oblivious Robots

Luna¹,

Uehara²,

Viglietta³

et al. 2020

Preprint

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show abstract

“…The underlying domain which is traversed by the robots is a continuous curve (in our case an infinite line) and the robots may exploit a particular characteristic, e.g., different identifiers, speeds, or their initial location, to achieve rendezvous. For example, in several papers the robots make use of the fact that they have different speeds, as in the paper [17], as well as in the work on probabilistic rendezvous on a cycle [22]. Rendezvous on a cycle for multiple robots with different speeds is studied in [19], and rendezvous in arbitrary graphs for two robots with different speeds in [24].…”

Section: Related Workmentioning

confidence: 99%

Rendezvous on a Line by Location-Aware Robots Despite the Presence of Byzantine Faults

Chuangpishit

Czyzowicz

Kranakis

et al. 2017

Algorithms for Sensor Systems

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Abstract. A set of mobile robots is placed at points of an infinite line. The robots are equipped with GPS devices and they may communicate their positions on the line to a central authority. The collection contains an unknown subset of "spies", i.e., byzantine robots, which are indistinguishable from the non-faulty ones. The set of the non-faulty robots need to rendezvous in the shortest possible time in order to perform some task, while the byzantine robots may try to delay their rendezvous for as long as possible. The problem facing a central authority is to determine trajectories for all robots so as to minimize the time until the non-faulty robots have rendezvoused. The trajectories must be determined without knowledge of which robots are faulty. Our goal is to minimize the competitive ratio between the time required to achieve the first rendezvous of the non-faulty robots and the time required for such a rendezvous to occur under the assumption that the faulty robots are known at the start. We provide a bounded competitive ratio algorithm, where the central authority is informed only of the set of initial robot positions, without knowing which ones or how many of them are faulty. When an upper bound on the number of byzantine robots is known to the central authority, we provide algorithms with better competitive ratios. In some instances we are able to show these algorithms are optimal.

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Rendezvous of Many Agents with Different Speeds in a Cycle

Huus

Kranakis

2015

Ad-Hoc, Mobile, and Wireless Networks

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Randomized Rendezvous Algorithms for Agents on a Ring with Different Speeds

Cited by 7 publications

References 32 publications

Gathering on a Circle with Limited Visibility by Anonymous Oblivious Robots

Gathering on a Circle with Limited Visibility by Anonymous Oblivious Robots

Rendezvous on a Line by Location-Aware Robots Despite the Presence of Byzantine Faults

Rendezvous of Many Agents with Different Speeds in a Cycle

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