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Coalescing Walks on Rotor-Router Systems

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Structural Information and Communication Complexity (SIROCCO 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9439))

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Abstract

We consider the rotor-router mechanism for distributing particles in an undirected graph. If the last particle passing through a vertex v took an edge (v,u), then the next time a particle is at v, it will leave v along the next edge (v,w) according to a fixed cyclic order of edges adjacent to v. The system works in synchronized steps and when two or more particles meet at the same vertex, they coalesce into one particle. A k-particle configuration of such a system is stable, if it does not lead to any coalescing. For 2 ≤ k ≤ n, we give the full characterization of stable k-particle configurations for cycles. We also show sufficient conditions for regular graphs with n vertices to admit n-particle stable configurations.

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Authors and Affiliations

  1. Department of Informatics, King’s College London, London, United Kingdom

    Colin Cooper, Tomasz Radzik & Nicolás Rivera

  2. Theoretical Computer Science Group, Department of Informatics, Kyushu University, Fukuoka, Japan

    Takeharu Shiraga

Authors
  1. Colin Cooper
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  2. Tomasz Radzik
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  3. Nicolás Rivera
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  4. Takeharu Shiraga
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Corresponding author

Correspondence to Colin Cooper .

Editor information

Editors and Affiliations

  1. Dept of Mathematics and Comp Science, Paderborn University, Paderborn, Nordrhein-Westfalen, Germany

    Christian Scheideler

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Cooper, C., Radzik, T., Rivera, N., Shiraga, T. (2015). Coalescing Walks on Rotor-Router Systems. In: Scheideler, C. (eds) Structural Information and Communication Complexity. SIROCCO 2015. Lecture Notes in Computer Science(), vol 9439. Springer, Cham. https://doi.org/10.1007/978-3-319-25258-2_31

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  • DOI: https://doi.org/10.1007/978-3-319-25258-2_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25257-5

  • Online ISBN: 978-3-319-25258-2

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