Dispersion of mobile robots on graphs in the asynchronous model

The dispersion problem on graphs requires k robots placed arbitrarily at the n nodes of an anonymous graph, where k≤n, to coordinate with each other to reach a final configuration in which each robot is at a distinct node of the graph. The dispersion problem is important due to its relationship to g...

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Bibliographic Details
Published in:Theoretical computer science Vol. 1044; p. 115272
Main Author: Kshemkalyani, Ajay D.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.08.2025
Subjects:
Dispersion
Distributed algorithm
Graph algorithm
Graph exploration
Mobile robot
Mobile robot
Graph exploration
Dispersion
Graph algorithm
Distributed algorithm
ISSN:0304-3975
Online Access:Get full text
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Summary:The dispersion problem on graphs requires k robots placed arbitrarily at the n nodes of an anonymous graph, where k≤n, to coordinate with each other to reach a final configuration in which each robot is at a distinct node of the graph. The dispersion problem is important due to its relationship to graph exploration by mobile robots, scattering on a graph, and load balancing on a graph. Prior work on solving dispersion assumed the synchronous model. We propose four algorithms to solve dispersion on graphs in the asynchronous model. The first two algorithms require O(klog⁡Δ) bits at each robot and O(min⁡(m,kΔ)) steps running time, where m is the number of edges and Δ is the maximum degree of the graph. The algorithms differ in what, where, and how data structures are maintained. The third algorithm has a space usage of O(max⁡(min⁡(D,k)⋅log⁡Δ,log⁡D)) bits at each robot and uses O(Δmin⁡(D,k)+1) steps, where D is the graph diameter. The fourth algorithm has a space usage of O(max⁡(log⁡k,log⁡Δ)) bits at each robot and uses O(min⁡(m,kΔ)⋅k) steps. In contrast with existing works which all assume the synchronous model, these are the first algorithms to solve dispersion in the weaker but more realistic asynchronous model.
ISSN:0304-3975
DOI:10.1016/j.tcs.2025.115272