Computing Without Communicating: Ring Exploration by Asynchronous Oblivious Robots

Flocchini, Paola; Ilcinkas, David; Pełc, Andrzej; Santoro, Nicola

doi:10.1007/s00453-011-9611-5

Cited by 80 publications

(80 citation statements)

References 39 publications

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“…This task is challenging because the ring is unoriented and the agents cannot ''remember'' the direction of their last move (otherwise, they could simply continue forward). Considering deterministic algorithms, Flocchini et al [11] have shown that the problem is unsolvable if n and k are co-prime. They have also provided an algorithm which solves the problem otherwise.…”

Section: Related Workmentioning

confidence: 99%

Uniform multi-agent deployment on a ring

Elor

Bruckstein

2011

Theoretical Computer Science

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a b s t r a c tWe consider two variants of the task of spreading a swarm of agents uniformly on a ring graph. Ant-like oblivious agents having limited capabilities are considered. The agents are assumed to have little memory, they all execute the same algorithm and no direct communication is allowed between them. Furthermore, the agents do not possess any global information. In particular, the size of the ring (n) and the number of agents in the swarm (k) are unknown to them. The agents are assumed to operate on an unweighted ring graph. Every agent can measure the distance to his two neighbors on the ring, up to a limited range of V edges.The first task considered, is dynamical (i.e. in motion) uniform deployment on the ring.We show that if either the ring is unoriented, or the visibility range is less than ⌊n/k⌋, this is an impossible mission for the agents. Then, for an oriented ring and V ≥ ⌈n/k⌉, we propose an algorithm which achieves the deployment task in optimal time. The second task discussed, called quiescent spread, requires the agents to spread uniformly over the ring and stop moving. We prove that under our model, in which every agent can measure the distance only to his two neighbors, this task is impossible. Subsequently, we propose an algorithm which achieves quiescent but only almost uniform spread. The algorithms we present are scalable and robust. In case the environment (the size of the ring) or the number of agents changes during the run, the swarm adapts and re-deploys without requiring any outside interference.

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Section: Related Workmentioning

confidence: 99%

Uniform multi-agent deployment on a ring

Elor

Bruckstein

2011

Theoretical Computer Science

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“…As mentioned previously, our scenario for the graph world has been previously used in [17,18] in the context of gathering and in [12,13] in the context of exploration. Proof.…”

Section: Related Workmentioning

confidence: 99%

“…In [17,18] the related problem of gathering was investigated on a ring: robots starting from different locations have to meet in one node. In [12,13] the focus was on exploration, as in the present paper. In [12] the authors investigated the sizes of teams of robots capable of exploring trees: it was proved that there are n-node trees of maximum degree 4 where Ω(n) robots are necessary for exploration and that all trees of maximum degree 3 can be explored by O ( log n log log n ) robots.…”

mentioning

confidence: 97%

“…The above scenario has been used, for example, in [12,13,17,18]. In [17,18] the related problem of gathering was investigated on a ring: robots starting from different locations have to meet in one node.…”

mentioning

confidence: 99%

“…This left open the analogous problem on trees of maximum degree 2, i.e., the lines, that are the focus of the present paper. In [13] the focus was on sizes of teams capable of exploring an n-node cycle. It was shown that the minimum number of robots that can explore a ring of size n is O (log n) and that Ω(log n) robots are necessary for arbitrarily large n. Finally, in [6] the authors investigated a similar but stronger model with labeled edges and provided necessary and sufficient conditions for explorability of arbitrary graphs for k = 3, 4 robots and k > 4 odd robots.…”

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confidence: 99%

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How many oblivious robots can explore a line

Flocchini

Ilcinkas

Pełc

et al. 2011

Information Processing Letters

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International audienceWe consider the problem of exploring an anonymous line by a team of k identical, oblivious, asynchronous deterministic mobile robots that can view the environment but cannot communicate. We completely characterize sizes of teams of robots capable of exploring a n-node line. For k= 5, or k=4 and n is odd. For all values of k for which exploration is possible, we give an exploration algorithm. For all others, we prove an impossibility result

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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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Computing Without Communicating: Ring Exploration by Asynchronous Oblivious Robots

Cited by 80 publications

References 39 publications

Uniform multi-agent deployment on a ring

Uniform multi-agent deployment on a ring

How many oblivious robots can explore a line

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

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