The multi-agent rotor-router on the ring: a deterministic alternative to parallel random walks.
Saved in:
| Title: | The multi-agent rotor-router on the ring: a deterministic alternative to parallel random walks. |
|---|---|
| Authors: | Klasing, Ralf1 ralf.klasing@labri.fr, Kosowski, Adrian2 adrian.kosowski@inria.fr, Pająk, Dominik3 dominik.pajak@pwr.edu.pl, Sauerwald, Thomas4 thomas.sauerwald@cl.cam.ac.uk |
| Source: | Distributed Computing. Apr2017, Vol. 30 Issue 2, p127-148. 22p. |
| Subjects: | Network routers, Internetworking devices, Network hubs, Wireless communications, Wireless channels |
| Abstract: | The rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, an agent is initially placed at one of the nodes of the graph. Each node maintains a cyclic ordering of its outgoing arcs, and during successive visits of the agent, propagates it along arcs chosen according to this ordering in round-robin fashion. The behavior of the rotor-router is fully deterministic but its performance characteristics (cover time, return time) closely resemble the expected values of the corresponding parameters of the random walk. In this work we consider the setting in which multiple, indistinguishable agents are deployed in parallel in the nodes of the graph, and move around the graph in synchronous rounds, interacting with a single rotor-router system. We propose new techniques which allow us to perform a theoretical analysis of the multi-agent rotor-router model, and to compare it to the scenario of parallel independent random walks in a graph. Our main results concern the n-node ring, and suggest a strong similarity between the performance characteristics of this deterministic model and random walks. We show that on the ring the rotor-router with k agents admits a cover time of between $$\varTheta (n^2 / k^2)$$ in the best case and $$\varTheta (n^2 / \log k)$$ in the worst case, depending on the initial locations of the agents, and that both these bounds are tight. The corresponding expected value of the cover time for k random walks, depending on the initial locations of the walkers, is proven to belong to a similar range, namely between $$\varTheta (n^2 / (k^2/\log ^2 k))$$ and $$\varTheta (n^2 / \log k)$$ . Finally, we study the limit behavior of the rotor-router system. We show that, once the rotor-router system has stabilized, all the nodes of the ring are always visited by some agent every $$\varTheta (n / k)$$ steps, regardless of how the system was initialized. This asymptotic bound corresponds to the expected time between successive visits to a node in the case of k random walks. All our results hold up to a polynomially large number of agents ( $$1 \le k < n^{1/11}$$ ). [ABSTRACT FROM AUTHOR] |
| Copyright of Distributed Computing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 122987732 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: The multi-agent rotor-router on the ring: a deterministic alternative to parallel random walks. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Klasing%2C+Ralf%22">Klasing, Ralf</searchLink><relatesTo>1</relatesTo><i> ralf.klasing@labri.fr</i><br /><searchLink fieldCode="AR" term="%22Kosowski%2C+Adrian%22">Kosowski, Adrian</searchLink><relatesTo>2</relatesTo><i> adrian.kosowski@inria.fr</i><br /><searchLink fieldCode="AR" term="%22Pająk%2C+Dominik%22">Pająk, Dominik</searchLink><relatesTo>3</relatesTo><i> dominik.pajak@pwr.edu.pl</i><br /><searchLink fieldCode="AR" term="%22Sauerwald%2C+Thomas%22">Sauerwald, Thomas</searchLink><relatesTo>4</relatesTo><i> thomas.sauerwald@cl.cam.ac.uk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Distributed+Computing%22">Distributed Computing</searchLink>. Apr2017, Vol. 30 Issue 2, p127-148. 22p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Network+routers%22">Network routers</searchLink><br /><searchLink fieldCode="DE" term="%22Internetworking+devices%22">Internetworking devices</searchLink><br /><searchLink fieldCode="DE" term="%22Network+hubs%22">Network hubs</searchLink><br /><searchLink fieldCode="DE" term="%22Wireless+communications%22">Wireless communications</searchLink><br /><searchLink fieldCode="DE" term="%22Wireless+channels%22">Wireless channels</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, an agent is initially placed at one of the nodes of the graph. Each node maintains a cyclic ordering of its outgoing arcs, and during successive visits of the agent, propagates it along arcs chosen according to this ordering in round-robin fashion. The behavior of the rotor-router is fully deterministic but its performance characteristics (cover time, return time) closely resemble the expected values of the corresponding parameters of the random walk. In this work we consider the setting in which multiple, indistinguishable agents are deployed in parallel in the nodes of the graph, and move around the graph in synchronous rounds, interacting with a single rotor-router system. We propose new techniques which allow us to perform a theoretical analysis of the multi-agent rotor-router model, and to compare it to the scenario of parallel independent random walks in a graph. Our main results concern the n-node ring, and suggest a strong similarity between the performance characteristics of this deterministic model and random walks. We show that on the ring the rotor-router with k agents admits a cover time of between $$\varTheta (n^2 / k^2)$$ in the best case and $$\varTheta (n^2 / \log k)$$ in the worst case, depending on the initial locations of the agents, and that both these bounds are tight. The corresponding expected value of the cover time for k random walks, depending on the initial locations of the walkers, is proven to belong to a similar range, namely between $$\varTheta (n^2 / (k^2/\log ^2 k))$$ and $$\varTheta (n^2 / \log k)$$ . Finally, we study the limit behavior of the rotor-router system. We show that, once the rotor-router system has stabilized, all the nodes of the ring are always visited by some agent every $$\varTheta (n / k)$$ steps, regardless of how the system was initialized. This asymptotic bound corresponds to the expected time between successive visits to a node in the case of k random walks. All our results hold up to a polynomially large number of agents ( $$1 \le k < n^{1/11}$$ ). [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Distributed Computing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=122987732 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00446-016-0282-y Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 127 Subjects: – SubjectFull: Network routers Type: general – SubjectFull: Internetworking devices Type: general – SubjectFull: Network hubs Type: general – SubjectFull: Wireless communications Type: general – SubjectFull: Wireless channels Type: general Titles: – TitleFull: The multi-agent rotor-router on the ring: a deterministic alternative to parallel random walks. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Klasing, Ralf – PersonEntity: Name: NameFull: Kosowski, Adrian – PersonEntity: Name: NameFull: Pająk, Dominik – PersonEntity: Name: NameFull: Sauerwald, Thomas IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2017 Type: published Y: 2017 Identifiers: – Type: issn-print Value: 01782770 Numbering: – Type: volume Value: 30 – Type: issue Value: 2 Titles: – TitleFull: Distributed Computing Type: main |
| ResultId | 1 |
