Uniform scattering of autonomous mobile robots in a grid

Barrière, Lali; Flocchini, Paola; Mesa-Barrameda, Eduardo; Santoro, Nicola

doi:10.1109/ipdps.2009.5160871

Cited by 30 publications

(11 citation statements)

References 16 publications

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“…Another problem related to Dispersion is the scattering of k robots in graphs. This problem has been studied for rings [9,20] and grids [3]. Recently, Poudel and Sharma [19] provided a Θ( √ n)-time algorithm for uniform scattering in a grid [7].…”

Section: Algorithm Memory Per Robot Time (In Rounds) (In Bits)mentioning

confidence: 99%

“…Algorithm 1: Algorithm Graph Disperse(k) to solve Dispersion. 1 if i is alone at node then 2 i.settled ← 1; do not set i.treelabel 3 for pass = 1, log k do 4 Stage 1 (Graph DFS: for group dispersion of unsettled robots) 5 for round = 0, min(4m − 2n + 2, k∆) do 6 if visited node is free then 7 highest ID robot r settles; r.treelabel ← x.ID, where x is robot with lowest ID 8 x continues its DFS after r sets its parent, child for DFS of x reset parent, child, treelabel, mult, home // Lexico-priority: (mult, treelabel/ID). Higher mult is higher priority; if mult is equal, lower treelabel/ID has higher priority.…”

Section: Stagementioning

confidence: 99%

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Fast Dispersion of Mobile Robots on Arbitrary Graphs

Kshemkalyani

Molla

Sharma

2019

Algorithms for Sensor Systems

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The mobile robot dispersion problem on graphs asks k ≤ n robots placed initially arbitrarily on the nodes of an n-node anonymous graph to reposition autonomously to reach a configuration in which each robot is on a distinct node of the graph. This problem is of significant interest due to its relationship to other fundamental robot coordination problems, such as exploration, scattering, load balancing, and relocation of self-driven electric cars (robots) to recharge stations (nodes). In this paper, we provide two novel deterministic algorithms for dispersion, one for arbitrary graphs and another for grid graphs, in a synchronous setting where all robots perform their actions in every time step. Our algorithm for arbitrary graphs has O(min(m, k∆) · log k) steps runtime using O(log n) bits of memory at each robot, where m is the number of edges and ∆ is the maximum degree of the graph. This is an exponential improvement over the O(mk) steps best previously known algorithm. In particular, the runtime of our algorithm is optimal (up to a O(log k) factor) in constant-degree arbitrary graphs. Our algorithm for grid graphs has O(min(k, √ n)) steps runtime using Θ(log k) bits at each robot. This is the first algorithm for dispersion in grid graphs. Moreover, this algorithm is optimal for both memory and time when k = Ω(n). problem). This problem has many practical applications, for example, in relocating selfdriven electric cars (robots) to recharge stations (nodes), assuming that the cars have smart devices to communicate with each other to find a free/empty charging station [1,16]. This problem is also important due to its relationship to many other well-studied autonomous robot coordination problems, such as exploration, scattering, load balancing, covering, and self-deployment [1,16]. One of the key aspects of mobile-robot research is to understand how to use the resource-limited robots to accomplish some large task in a distributed manner [10,11]. In this paper, we study the trade-off between memory requirement of robots and the time to solve Dispersion on graphs.Augustine and Moses Jr.[1] studied Dispersion assuming k = n. They proved a memory lower bound of Ω(log n) bits at each robot and a time lower bound of Ω(D) (Ω(n) in arbitrary graphs) for any deterministic algorithm in any graph, where D is the diameter of the graph. They then provided deterministic algorithms using O(log n) bits at each robot to solve Dispersion on lines, rings, and trees in O(n) time. For arbitrary graphs, they provided two algorithms, one using O(log n) bits at each robot with O(mn) time and another using O(n log n) bits at each robot with O(m) time, where m is the number of edges in the graph. Recently, Kshemkalyani and Ali [16] provided an Ω(k) time lower bound for arbitrary graphs for k ≤ n. They then provided three deterministic algorithms for Dispersion in arbitrary graphs: (i) The first algorithm using O(k log ∆) bits at each robot with O(m) time, (ii) The second algorithm using O(D log ∆) bits at each robot with O(∆ D ) time, and ...

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Section: Algorithm Memory Per Robot Time (In Rounds) (In Bits)mentioning

confidence: 99%

Section: Stagementioning

confidence: 99%

Fast Dispersion of Mobile Robots on Arbitrary Graphs

Kshemkalyani

Molla

Sharma

2019

Algorithms for Sensor Systems

View full text Add to dashboard Cite

show abstract

“…Another problem related to D is the sca ering of k robots in an n-node graph. is problem has been studied for rings [11,24] and grids [3]. Recently, Poudel and Sharma [23] provided a Θ( √ n)-time algorithm for uniform sca ering in a grid [8].…”

Section: Algorithmmentioning

confidence: 99%

Dispersion of Mobile Robots in the Global Communication Model

Kshemkalyani

Molla

Sharma

2020

Proceedings of the 21st International Conference on Distributed Computing and Networking

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e dispersion problem on graphs asks k ≤ n robots placed initially arbitrarily on the nodes of an n-node anonymous graph to reposition autonomously to reach a con guration in which each robot is on a distinct node of the graph. is problem is of signi cant interest due to its relationship to other fundamental robot coordination problems, such as exploration, sca ering, load balancing, and relocation of self-driven electric cars (robots) to recharge stations (nodes). In this paper, we consider dispersion in the global communication model where a robot can communicate with any other robot in the graph (but the graph is unknown to robots). We provide three novel deterministic algorithms, two for arbitrary graphs and one for arbitrary trees, in a synchronous se ing where all robots perform their actions in every time step. For arbitrary graphs, our rst algorithm is based on a DFS traversal and guarantees O(min(m, k∆)) steps runtime using Θ(log(max(k, ∆))) bits at each robot, where m is the number of edges and ∆ is the maximum degree of the graph. e second algorithm for arbitrary graphs is based on a BFS traversal and guarantees O(max(D, k)∆(D + ∆)) steps runtime using O(max(D, ∆ log k)) bits at each robot, where D is the diameter of the graph. e algorithm for arbitrary trees is also based on a BFS travesal and guarantees O(D max(D, k)) steps runtime using O(max(D, ∆ log k)) bits at each robot. Our results are signi cant improvements compared to the existing results established in the local communication model where a robot can communication only with other robots present at the same node. Particularly, the DFS-based algorithm is optimal for both memory and time in constant-degree arbitrary graphs. e BFS-based algorithm for arbitrary trees is optimal with respect to runtime when k ≤ O(D).

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“…However, they cannot stop on edges. Several gathering problems are defined on graphs, such as gathering in trees [17], rings [12] and grids [4]. In this paper, we will discuss gathering in a tree with some further limitations imposed on the robots, specifically; their observing capabilities.…”

Section: Introductionmentioning

confidence: 99%

Gathering of Asynchronous Mobile Robots in a Tree

Bhaumik

Chaudhuri

2015

2015 Applications and Innovations in Mobile Computing (AIMoC)

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This paper addresses a robot-based distributed model which makes use of a group of small, inexpensive, identical, oblivious mobile robots placed in nodes of an anonymous and unoriented tree. The robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), takes a decision whether to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case makes an instantaneous move to this neighbour (Move). Cycles are performed asynchronously for each robot. In this paper, we present a distributed algorithm by which k robots deterministically gather at a single uniquely marked node in a tree with n nodes. The robots have limited visibility and have no common agreement in coordinate axes.

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Uniform scattering of autonomous mobile robots in a grid

Cited by 30 publications

References 16 publications

Fast Dispersion of Mobile Robots on Arbitrary Graphs

Fast Dispersion of Mobile Robots on Arbitrary Graphs

Dispersion of Mobile Robots in the Global Communication Model

Gathering of Asynchronous Mobile Robots in a Tree

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