Collaborative dispersion by silent robots

In the dispersion problem, a set of k co-located mobile robots must relocate themselves in distinct nodes of an unknown network. The network is modeled as an anonymous graph G=(V,E), where the graph's nodes are not labeled. The edges incident to a node v with degree d are labeled with port numb...

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Vydané v:Journal of parallel and distributed computing Ročník 188; s. 104852
Hlavní autori: Gorain, Barun, Mandal, Partha Sarathi, Mondal, Kaushik, Pandit, Supantha
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 01.06.2024
Predmet:
Anonymous graphs
Deterministic algorithm
Dispersion
Mobile robots
Time and memory complexity
Deterministic algorithm
Mobile robots
Anonymous graphs
Time and memory complexity
Dispersion
ISSN:0743-7315, 1096-0848
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Popis
Shrnutí:In the dispersion problem, a set of k co-located mobile robots must relocate themselves in distinct nodes of an unknown network. The network is modeled as an anonymous graph G=(V,E), where the graph's nodes are not labeled. The edges incident to a node v with degree d are labeled with port numbers in the range {0,1,…,d−1} at v. The robots have unique IDs in the range [0,L], where L≥k, and are initially placed at a source node s. The task of the dispersion was traditionally achieved based on the assumption of two types of communication abilities: (a) when some robots are at the same node, they can communicate by exchanging messages between them, and (b) any two robots in the network can exchange messages between them. This paper investigates whether this communication ability among co-located robots is absolutely necessary to achieve dispersion. We establish that even in the absence of the ability of communication, the task of the dispersion by a set of mobile robots can be achieved in a much weaker model, where a robot at a node v has access to following very restricted information at the beginning of any round: (1) am I alone at v? (2) did the number of robots at v increase or decrease compared to the previous round? We propose a deterministic distributed algorithm that achieves the dispersion on any given graph G=(V,E) in time O(klog⁡L+k2log⁡Δ), where Δ is the maximum degree of a node in G. Further, each robot uses O(log⁡L+log⁡Δ) additional memory, i.e., memory other than the memory required to store its id. We also prove that the task of the dispersion cannot be achieved by a set of mobile robots with o(log⁡L+log⁡Δ) additional memory. •We study the problem of dispersion on a network by a set of silent robots.•Any two robots can not communicate, but can sense some local activities.•We achieve dispersion from a rooted configuration with optimal memory.
ISSN:0743-7315
1096-0848
DOI:10.1016/j.jpdc.2024.104852