Fast Uniform Scattering on a Grid for Asynchronous Oblivious Robots

Poudel, Pavan; Sharma, Gokarna

doi:10.1007/978-3-030-64348-5_17

Cited by 13 publications

(7 citation statements)

References 22 publications

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“…In addition, when robots equipped with resources such as foods are deployed uniformly in a disaster area, victims can access to the resources quickly. So far, the uniform deployment problem for mobile robots has been considered in cycles (i.e., the continuous model), 10 rings (i.e., the discrete model), 11 and grid networks (again, the discrete model) 9,12‐14 . In grids, it was argued you can achieve uniform deployment faster 12 or better 14 using luminous robots (uniform deployment in grids is nevertheless feasible by oblivious robots 9 ).…”

Section: Introductionmentioning

confidence: 99%

“…So far, the uniform deployment problem for mobile robots has been considered in cycles (i.e., the continuous model), 10 rings (i.e., the discrete model), 11 and grid networks (again, the discrete model). 9,[12][13][14] In grids, it was argued you can achieve uniform deployment faster 12 or better 14 using luminous robots…”

mentioning

confidence: 99%

“…D'Emidio et al 16 consider the solvability of several problems for luminous robots in the graph environment, focusing on the relationship between synchronicity and the necessary number of light colors to solve problems. Recently, Poudel and Sharma 13 improved the time complexity of uniform deployment on grids for robots without light colors (i.e., oblivious robots). A separate research track considered the uniform deployment problem in ring networks for another mobile entity called mobile agents, [17][18][19] which have persistent memory but cannot observe others' positions unless they are located on the same node.…”

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confidence: 99%

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Semi‐uniform deployment of mobile robots in perfect ℓ$$ \ell $$‐ary trees

Shibata

Tixeuil

2022

Concurrency and Computation

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Summary In this paper, we consider the problem of semi‐uniform deployment for mobile robots in perfect ℓ$$ \ell $$‐ary trees. This problem requires robots to spread in the tree so that, for some positive integer d$$ d $$ and some fixed integer sfalse(0≤s≤dprefix−1false)$$ s\left(0\le s\le d-1\right) $$, each node of depth s+djfalse(j≥0false)$$ s+ dj\left(j\ge 0\right) $$ is occupied by a robot. Robots have an infinite visibility range but are opaque, and each robot can emit a light color visible to itself and other robots, taken from a set of κ$$ \kappa $$ colors, at each time step. Then, we clarify the solvability of the semi‐uniform deployment problem, focusing on the number of available light colors. First, we consider robots with κ=1$$ \kappa =1 $$. In this setting, we show that there is no collision‐free algorithm to solve the problem. Next, relax the number of available light colors, that is, we consider robots with κ=2$$ \kappa =2 $$. In this setting, we propose a collision‐free algorithm that can solve the problem. From these results, we can show that the semi‐uniform deployment problem can be solved when κ≥2$$ \kappa \ge 2 $$, and our proposed algorithm is optimal with respect to the number of used light colors (i.e., 2).

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Semi‐uniform deployment of mobile robots in perfect ℓ$$ \ell $$‐ary trees

Shibata

Tixeuil

2022

Concurrency and Computation

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“…where k ≥ 2, d ≥ 2, the number of robots is (k + 1) 2 , and that each robot knows k and d. They also assume that each robot has internal lights with six colors and that their visible radius is 2d. Under the same assumptions as Barrière et al [3], Poudel et al [31] proposed an algorithm needing O(1) bit memory per robot, assuming a visibility radius of 2 max{d, k}. By contrast, we don't assume a common orientation, we use seven or three full lights colors, and the size of the grid is arbitrary and unknown.…”

Section: Introductionmentioning

confidence: 99%

An Asynchronous Maximum Independent Set Algorithm by Myopic Luminous Robots on Grids

Kamei¹,

Tixeuil²

2020

Preprint

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We consider the problem of constructing a maximum independent set with mobile myopic luminous robots on a grid network whose size is finite but unknown to the robots. In this setting, the robots enter the grid network one-byone from a corner of the grid, and they eventually have to be disseminated on the grid nodes so that the occupied positions form a maximum independent set of the network. We assume that robots are asynchronous, anonymous, silent, and they execute the same distributed algorithm. In this paper, we propose two algorithms: The first one assumes the number of light colors of each robot is three and the visible range is two, but uses additional strong assumptions of port-numbering for each node. To delete this assumption, the second one assumes the number of light colors of each robot is seven and the visible range is three. In both algorithms, the number of movements is O(n(L + l)) steps where n is the number of nodes and L and l are the grid dimensions.

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“…This problem has been mainly studied for rings [10,27] and grids [3]. Recently, Poudel and Sharma [25,26] provided improved time algorithms for uniform scattering on grids.…”

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confidence: 99%

Near-Optimal Dispersion on Arbitrary Anonymous Graphs

Kshemkalyani,

Sharma

2021

Preprint

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Given an undirected, anonymous, port-labeled graph of memoryless nodes, edges, and degree Δ, we consider the problem of dispersing ≤ robots (or tokens) positioned initially arbitrarily on one or more nodes of the graph to exactly different nodes of the graph, one on each node. The objective is to simultaneously minimize time to achieve dispersion and memory requirement at each robot. If all robots are positioned initially on a single node, depth first search (DFS) traversal solves this problem in (min{ , Δ}) time with Θ(log( + Δ)) bits at each robot. However, if robots are positioned initially on multiple nodes, the best previously known algorithm solves this problem in (min{ , Δ} • log ℓ) time storing Θ(log( + Δ)) bits at each robot, where ℓ ≤ /2 is the number of multiplicity nodes in the initial configuration. In this paper, we present a novel multi-source DFS traversal algorithm solving this problem in (min{ , Δ}) time with Θ(log( +Δ)) bits at each robot, improving the time bound of the best previously known algorithm by (log ℓ) and matching asymptotically the single-source DFS traversal bounds. This is the first algorithm for dispersion that is optimal in both time and memory in arbitrary anonymous graphs of constant degree, Δ = (1). Furthermore, the result holds in both synchronous and asynchronous settings. CCS CONCEPTS• Mathematics of computing → Graph algorithms; • Computing methodologies → Distributed algorithms; • Computer systems organization → Robotics.

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Fast Uniform Scattering on a Grid for Asynchronous Oblivious Robots

Cited by 13 publications

References 22 publications

Semi‐uniform deployment of mobile robots in perfect ℓ$$ \ell $$‐ary trees

Semi‐uniform deployment of mobile robots in perfect ℓ$$ \ell $$‐ary trees

An Asynchronous Maximum Independent Set Algorithm by Myopic Luminous Robots on Grids

Near-Optimal Dispersion on Arbitrary Anonymous Graphs

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