Coalescing Walks on Rotor-Router Systems

  • Colin Cooper
  • Tomasz Radzik
  • Nicolás Rivera
  • Takeharu Shiraga
Conference paper

DOI: 10.1007/978-3-319-25258-2_31

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9439)
Cite this paper as:
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 2014. Lecture Notes in Computer Science, vol 9439. Springer, Cham

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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Colin Cooper
    • 1
  • Tomasz Radzik
    • 1
  • Nicolás Rivera
    • 1
  • Takeharu Shiraga
    • 2
  1. 1.Department of InformaticsKing’s College LondonLondonUnited Kingdom
  2. 2.Theoretical Computer Science Group, Department of InformaticsKyushu UniversityFukuokaJapan

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