Sublinear-time mutual visibility for fat oblivious robots

Poudel, Pavan; Sharma, Gokarna; Aljohani, Aisha

doi:10.1145/3288599.3288602

Cited by 8 publications

(7 citation statements)

References 15 publications

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“…robots, to ensure that there is enough space for every interior robot to become a corner robot. Poudel et al [16] showed that this length suffices. This is the only step where the corner robots temporarily need to know n, in order to compare it to the current edge lengths.…”

Section: The Interior Depletion Phasementioning

confidence: 97%

“…Poudel et al [16] studied the Mutual Visibility problem for fat robots on an infinite grid graph G and the robots have to reposition themselves on the vertices of the graph G. They provided two algorithms; the first one solves the Mutual Visibility problem in O( √ n) time under a centralized scheduler. The second one solves the same problem in Θ( √ n) time under a distributed scheduler, but only for some special instances.…”

Section: Related Workmentioning

confidence: 99%

“…Unfortunately, the techniques developed for point robots do not apply directly to the unit disk robots, due to the lack of collision avoidance. For unit disk robots, much progress has been made in solving the Mutual Visibility problem [1,2,3,6,7,12,16,17,20], however these approaches either require additional assumptions such as chirality, knowledge of n, or without avoiding collisions. Additionally, some approaches require a large number of colors and not all approaches bound the number of rounds needed.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Mutual Visibility Problem for Fat Robots

Alsaedi¹,

Gudmundsson²,

Renssen³

2022

Preprint

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Given a set of n ≥ 1 unit disk robots in the Euclidean plane, we consider the fundamental problem of providing mutual visibility to them: the robots must reposition themselves to reach a configuration where they all see each other. This problem arises under obstructed visibility, where a robot cannot see another robot if there is a third robot on the straight line segment between them. This problem was solved by Sharma et al. [17] in the luminous robots model, where each robot is equipped with an externally visible light that can assume colors from a fixed set of colors, using 9 colors and O(n) rounds. In this work, we present an algorithm that requires only 3 colors and O(n) rounds.

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Section: The Interior Depletion Phasementioning

confidence: 97%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Mutual Visibility Problem for Fat Robots

Alsaedi¹,

Gudmundsson²,

Renssen³

2022

Preprint

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show abstract

“…While fundamental problems in autonomous mobile robots like Gathering [4,7,11,14,26], Arbitrary Pattern Formation [5,6,21], and Mutual Visibility [1,27] have been studied in grid environments, the Circle Formation problem has only been studied on a continuous Euclidean plane. In the Circle Formation problem, robots must place themselves over a circumference of a circle.…”

Section: Earlier Workmentioning

confidence: 99%

Circle formation by asynchronous opaque robots on infinite grid

Adhikary

Kundu²,

2021

csci

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This paper presents a distributed algorithm for circle formation problem under the infinite grid environment by asynchronous mobile opaque robots. Initially all the robots are acquiring distinct positions and they have to form a circle over the grid. Movements of the robots are restricted only along the grid lines. They do not share any global co-ordinate system. Robots are controlled by an asynchronous adversarial scheduler that operates in Look-Compute-Move cycles. The robots are indistinguishable by their nature, do not have any memory of their past configurations and previous actions. We consider the problem under luminous model, where robots communicate via lights, other than that they do not have any external communication system. Our protocol solves the circle formation problem using seven colors. A subroutine of our algorithm also solves the line formation problem using three colors.

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“…Starting with this initial work, many papers have addressed the same problem (e.g., see [2,4,23]). Later, similar visibility problems were considered in different contexts, where the entities are "fat entities" modeled as disks in the Euclidean plane (e.g., see [24]) or are points on a grid based terrain and their movements are restricted only along grid lines (e.g., see [1]).…”

Section: Introductionmentioning

confidence: 99%

On the mutual visibility in Cartesian products and triangle-free graphs

Cicerone¹,

Stefano²,

Klavžar³

2021

Preprint

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Given a graph G = (V (G), E(G)) and a set P ⊆ V (G), the following concepts have been recently introduced: (i) two elements of P are mutually visible if there is a shortest path between them without further elements of P ; (ii) P is a mutual-visibility set if its elements are pairwise mutually visible; (iii) the mutual-visibility number of G is the size of any largest mutual-visibility set. In this work we continue to investigate about these concepts. We first focus on mutual-visibility in Cartesian products. For this purpose, too, we introduce and investigate independent mutual-visibility sets. Then, we characterize the triangle-free graphs with the mutual-visibility number equal to 3.

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Sublinear-time mutual visibility for fat oblivious robots

Cited by 8 publications

References 15 publications

The Mutual Visibility Problem for Fat Robots

The Mutual Visibility Problem for Fat Robots

Circle formation by asynchronous opaque robots on infinite grid

On the mutual visibility in Cartesian products and triangle-free graphs

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