On the Self-stabilization of Mobile Robots in Graphs

Blin, Lélia; Potop-Butucaru, Maria; Tixeuil, Sébastien

doi:10.1007/978-3-540-77096-1_22

Cited by 7 publications

(3 citation statements)

References 24 publications

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“…For example, a fault-tolerant rendezvous algorithm is proposed in [10], the algorithm uses whiteboards on nodes as well as persistent memory at each agent. In [5], the authors address the problem of self-stabilizing naming. They give a deterministic solution for tree and a probabilistic one for arbitrary graphs.…”

Section: Related Workmentioning

confidence: 99%

Asymptotically Optimal Deterministic Rendezvous

Carrier

Devismes

Petit

et al. 2011

Int. J. Found. Comput. Sci.

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In this paper, we address the deterministic rendezvous in graphs where k mobile agents, disseminated at different times and different nodes, have to meet in finite time at the same node. The mobile agents are autonomous, oblivious, labeled, and move asynchronously. Moreover, we consider an undirected anonymous connected graph. For this problem, we exhibit some asymptotical time and space lower bounds as well as some necessary conditions. We also propose an algorithm that is asymptotically optimal in both space and round complexities.

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Section: Related Workmentioning

confidence: 99%

Asymptotically Optimal Deterministic Rendezvous

Carrier

Devismes

Petit

et al. 2011

Int. J. Found. Comput. Sci.

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“…A few self-stabilizing algorithms were given for mobile agents to solve problems other than exploration. Blin, Potop-Butucaru, and Tixeuil [2] studied the self-stabilizing naming and leader election problem. Masuzawa and Tixeuil [5] gave a self-stabilizing gossiping algorithm.…”

Section: Related Workmentioning

confidence: 99%

Self-stabilizing Graph Exploration by a Single Agent

Sudo,

Ooshita,

Kamei

2020

Preprint

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In this paper, we give two self-stabilizing algorithms that solve graph exploration by a single (mobile) agent. The proposed algorithms are self-stabilizing: the agent running each of the algorithms visits all nodes starting from any initial configuration where the state of the agent and the states of all nodes are arbitrary and the agent is located at an arbitrary node. We evaluate algorithms with two metrics, the cover time, that is the number of moves required to visit all nodes, and the amount of space to store the state of the agent and the states of the nodes. The first algorithm is a randomized one. The cover time of this algorithm is optimal (i.e., O(m)) in expectation and it uses O(log n) bits for both the agent and each node, where n and m are the number of agents and the number of edges in a given graph, respectively. The second algorithm is deterministic. The cover time is O(m + nD), where D is the diameter of the graph. It uses O(log n) bits for the agent-memory and O(δ + log n) bits for the memory of each node with degree δ. We require the knowledge of an upper bound on n (resp. D) for the first (resp. the second) algorithm. However, this is a weak assumption from a practical point of view because the knowledge of any value ≥ n (resp. ≥ D) in O(poly(n)) is sufficient to obtain the above time and space complexity.

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“…Moreover, to the best of our knowledge, there exist no self-stabilizing algorithm for exploration either in a static or a dynamic environment. Note that there exist such fault-tolerant solutions in static graphs to other problems (e.g., naming and leader election [3]).…”

Section: Introductionmentioning

confidence: 99%

Self-stabilizing Robots in Highly Dynamic Environments

Bournat

Datta

Dubois

2016

Lecture Notes in Computer Science

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This paper deals with the classical problem of exploring a ring by a cohort of synchronous robots. We focus on the perpetual version of this problem in which it is required that each node of the ring is visited by a robot infinitely often.The challenge in this paper is twofold. First, we assume that the robots evolve in a highly dynamic ring, i.e., edges may appear and disappear unpredictably without any recurrence, periodicity, nor stability assumption. The only assumption we made (known as temporal connectivity assumption) is that each node is infinitely often reachable from any other node. Second, we aim at providing a self-stabilizing algorithm to the robots, i.e., the algorithm must guarantee an eventual correct behavior regardless of the initial state and positions of the robots.In this harsh environment, our contribution is to fully characterize, for each size of the ring, the necessary and sufficient number of robots to solve deterministically the problem.

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On the Self-stabilization of Mobile Robots in Graphs

Cited by 7 publications

References 24 publications

Asymptotically Optimal Deterministic Rendezvous

Asymptotically Optimal Deterministic Rendezvous

Self-stabilizing Graph Exploration by a Single Agent

Self-stabilizing Robots in Highly Dynamic Environments

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