Coalescing Walks on Rotor-Router Systems
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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 2014. Lecture Notes in Computer Science, vol 9439. Springer, Cham
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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