Mediated Population Protocols: Leader Election and Applications
Mediated population protocols are an extension of population protocols in which communication links, as well as agents, have internal states. We study the leader election problem and some applications in constant-state mediated population protocols. Depending on the power of the adversarial scheduler, our algorithms are either stabilizing or allow the agents to explicitly reach a terminal state.
We show how to elect a unique leader if the graph of the possible interactions between agents is complete (as in the traditional population protocol model) or a tree. Moreover, we prove that a leader can be elected in a complete bipartite graph if and only if the two sides have coprime size.
We then describe how to take advantage of the presence of a leader to solve the tasks of token circulation and construction of a shortest-path spanning tree of the network. Finally, we prove that with a leader we can transform any stabilizing protocol into a terminating one that solves the same task.
- 1.Alistarh, D., Gelashvili, R., Vojnovic, M.: Fast and exact majority in population protocols. In: 34th Annual ACM Symposium on Principles of Distributed Computing, PODC, pp. 47–56 (2015)Google Scholar
- 2.Angluin, D., Aspnes, J., Chan, M., Fischer, M.J., Jiang, H., Peralta, R.: Stably computable properties of network graphs. In: Prasanna, V.K., Iyengar, S.S., Spirakis, P.G., Welsh, M. (eds.) DCOSS 2005. LNCS, vol. 3560, pp. 63–74. Springer, Heidelberg (2005). doi: 10.1007/11502593_8 CrossRefGoogle Scholar
- 5.Angluin, D., Aspnes, J., Eisenstat, D.: Stably computable predicates are semilinear. In: 25th Annual ACM Symposium on Principles of Distributed Computing, PODC, pp. 292–299 (2006)Google Scholar
- 6.Beauquier, J., Blanchard, P., Burman, J.: Self-stabilizing leader election in population protocols over arbitrary communication graphs. In: Baldoni, R., Nisse, N., Steen, M. (eds.) OPODIS 2013. LNCS, vol. 8304, pp. 38–52. Springer, Cham (2013). doi: 10.1007/978-3-319-03850-6_4 CrossRefGoogle Scholar
- 10.Canepa, D., Potop-Butucaru, M.G.: Stabilizing leader election in population protocols, Research Report, inria-00166632 (2007)Google Scholar
- 11.Canepa, D., Potop-Butucaru, M.G.: Self-stabilizing tiny interaction protocols. In: 3rd International Workshop on Reliability, Availability, and Security, WRAS, pp. 1–6 (2010)Google Scholar
- 14.Di Luna, G.A., Flocchini, P., Izumi, T., Izumi, T., Santoro, N., Viglietta, G.: Population protocols with faulty interactions: the impact of a leader. arXiv:1611.06864 [cs.DC] (2016)