Arbitrary Pattern Formation on Infinite Regular Tessellation Graphs

Cicerone, Serafino; Fonso, Alessia Di; Stefano, Gabriele Di; Navarra, Alfredo

doi:10.1145/3427796.3427833

Cited by 11 publications

(3 citation statements)

References 33 publications

(29 reference statements)

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“…Recently, in [9], the authors have provided an algorithm for robots on a triangular grid to form any arbitrary pattern from any asymmetric initial configuration.…”

Section: Our Contributionmentioning

confidence: 99%

“…In their work, they have assumed that the target configuration can have multiplicities also. So the algorithm provided in [9] can be used for gathering where the target configuration contains only one location for each robot. But in their work, they have assumed the robots have full visibility which is impractical as in application it is impossible for robots to have an infinite vision.…”

Section: Our Contributionmentioning

confidence: 99%

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Time Optimal Gathering of Myopic Robots on an Infinite Triangular Grid

Goswami¹,

Sharma²,

Ghosh³

et al. 2022

Preprint

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This work deals with the problem of gathering of n oblivious mobile entities, called robots, with limited visibility, at a point (not known beforehand) placed on an infinite triangular grid. Earlier works of gathering mostly considered the robots either on a plane or on a circle or on a rectangular grid under both full and limited visibility. In the triangular grid, there are two works to the best of our knowledge. The first one is arbitrary pattern formation where full visibility is considered ([9]). The other one considers seven robots with 2-hop visibility that form a hexagon with one robot in the center of the hexagon in a collision-less environment under a fully synchronous scheduler ([26]). In this work, we first show that gathering on a triangular grid with 1-hop vision of robots is not possible even under a fully synchronous scheduler if the robots do not agree on any axes. So one axis agreement has been considered in this work (i.e., the robots agree on a direction and its orientation). With this capability of robots, this work shows that a swarm of any number of robots with 1-hop visibility can gather within a finite time even when the scheduler is asynchronous.

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“…Recently, in [9], the authors have provided an algorithm for robots on a triangular grid to form any arbitrary pattern from any asymmetric initial configuration.…”

Section: Our Contributionmentioning

confidence: 99%

Section: Our Contributionmentioning

confidence: 99%

Time Optimal Gathering of Myopic Robots on an Infinite Triangular Grid

Goswami¹,

Sharma²,

Ghosh³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…APF problem aims to design an algorithm such that robots move to a particular position and form a specific but arbitrary pattern which is already given to every robot as input. There is a vast literature of APF in both discrete and continuous domains ( [18,19,14,11,4,5,7,2,3,1,8,16,6]). Most of the works of APF in continuous domain considered on the Euclidean plane.…”

Section: Introductionmentioning

confidence: 99%

Arbitrary Pattern Formation on a Continuous Circle by Oblivious Robot Swarm

Mondal¹,

Goswami²,

Sharma³

et al. 2023

Preprint

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In the field of distributed system, Arbitrary Pattern Formation (APF) problem is an extensively studied problem. The purpose of APF is to design an algorithm to move a swarm of robots to a particular position on an environment (discrete or continuous) such that the swarm can form a specific but arbitrary pattern given previously to every robot as an input. In this paper the APF problem is discussed on continuous circle by a swarm of homogeneous, anonymous, oblivious, silent mobile robots with no chirality. The algorithm discussed here, can solve APF problem deterministically within O(n) epochs without collision under Semi Synchronous scheduler with n (where n is odd) mobile robots if the initial configuration is rotationally asymmetric. For any even number of robots (grater than three) the algorithm can be modified to a probabilistic one to solve APF. Also if the initial configuration is rotationally symmetric then APF problem can't be solved by any deterministic algorithm.

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Arbitrary Pattern Formation on Infinite Regular Tessellation Graphs

Cited by 11 publications

References 33 publications

Time Optimal Gathering of Myopic Robots on an Infinite Triangular Grid

Time Optimal Gathering of Myopic Robots on an Infinite Triangular Grid

Arbitrary Pattern Formation on a Continuous Circle by Oblivious Robot Swarm

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