Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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)
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
Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distrib. Comput. 18(4), 235–253 (2006)
Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. ACM Trans. Auton. Adapt. Syst. 3(4), 1–28 (2008)
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)
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
Beauquier, J., Burman, J., Clavière, S., Sohier, D.: Space-optimal counting in population protocols. In: Moses, Y. (ed.) DISC 2015. LNCS, vol. 9363, pp. 631–646. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48653-5_42
Beauquier, J., Burman, J., Kutten, S.: A self-stabilizing transformer for population protocols with covering. Theor. Comput. Sci. 412(33), 4247–4259 (2011)
Cai, S., Izumi, T., Wada, K.: How to prove impossibility under global fairness: on space complexity of self-stabilizing leader election on a population protocol model. Theor. Comput. Syst. 50(3), 433–445 (2012)
Canepa, D., Potop-Butucaru, M.G.: Stabilizing leader election in population protocols, Research Report, inria-00166632 (2007)
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)
Chatzigiannakis, I., Michail, O., Spirakis, P.G.: Stably decidable graph languages by mediated population protocols. In: Dolev, S., Cobb, J., Fischer, M., Yung, M. (eds.) SSS 2010. LNCS, vol. 6366, pp. 252–266. Springer, Heidelberg (2010). doi:10.1007/978-3-642-16023-3_21
Chatzigiannakis, I., Michail, O., Spirakis, P.G.: Mediated population protocols. Theor. Comput. Sci. 412(22), 2434–2450 (2011)
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)
Fischer, M., Jiang, H.: Self-stabilizing leader election in networks of finite-state anonymous agents. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 395–409. Springer, Heidelberg (2006). doi:10.1007/11945529_28
Mizoguchi, R., Hirotaka, O., Kijima, S., Yamashita, M.: On space complexity of self-stabilizing leader election in mediated population protocol. Distrib. Comput. 25(6), 451–460 (2012)
Shavit, N., Francez, N.: A new approach to detection of locally indicative stability. In: Kott, L. (ed.) ICALP 1986. LNCS, vol. 226, pp. 344–358. Springer, Heidelberg (1986). doi:10.1007/3-540-16761-7_84
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Das, S., Di Luna, G.A., Flocchini, P., Santoro, N., Viglietta, G. (2017). Mediated Population Protocols: Leader Election and Applications. In: Gopal, T., Jäger , G., Steila, S. (eds) Theory and Applications of Models of Computation. TAMC 2017. Lecture Notes in Computer Science(), vol 10185. Springer, Cham. https://doi.org/10.1007/978-3-319-55911-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-55911-7_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-55910-0
Online ISBN: 978-3-319-55911-7
eBook Packages: Computer ScienceComputer Science (R0)