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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| Vydáno v: | Theoretical computer science Ročník 1044; s. 115272 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.08.2025
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| ISSN: | 0304-3975 |
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| Abstract | 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(klogΔ) 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)⋅logΔ,logD)) 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(logk,logΔ)) 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. |
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| AbstractList | 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(klogΔ) 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)⋅logΔ,logD)) 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(logk,logΔ)) 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. |
| ArticleNumber | 115272 |
| Author | Kshemkalyani, Ajay D. |
| Author_xml | – sequence: 1 givenname: Ajay D. surname: Kshemkalyani fullname: Kshemkalyani, Ajay D. email: ajay@uic.edu organization: Department of Computer Science, University of Illinois Chicago, Chicago, IL 60607, USA |
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| Keywords | Mobile robot Graph exploration Dispersion Graph algorithm Distributed algorithm |
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ACM doi: 10.1145/1391289.1391291 – start-page: 12:1 year: 2020 ident: 10.1016/j.tcs.2025.115272_br0100 article-title: Dispersion of mobile robots in the global communication model – volume: vol. 80 start-page: 132:1 year: 2017 ident: 10.1016/j.tcs.2025.115272_br0160 article-title: Deterministic graph exploration with advice – volume: 48 start-page: 166 issue: 3 year: 2006 ident: 10.1016/j.tcs.2025.115272_br0120 article-title: Collective tree exploration publication-title: Networks doi: 10.1002/net.20127 – start-page: 228 year: 2019 ident: 10.1016/j.tcs.2025.115272_br0270 article-title: Time-optimal uniform scattering in a grid – volume: 123 start-page: 145 year: 2019 ident: 10.1016/j.tcs.2025.115272_br0220 article-title: Gathering of mobile robots with weak multiplicity detection in presence of crash-faults publication-title: J. Parallel Distrib. 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| Title | Dispersion of mobile robots on graphs in the asynchronous model |
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