Abstract
This paper concerns randomized leader election in synchronous distributed networks. A distributed leader election algorithm is presented for complete n-node networks that runs in O(1) rounds and (with high probability) takes only \(O(\sqrt{n}\log^{3/2} n)\) messages to elect a unique leader (with high probability). This algorithm is then extended to solve leader election on any connected non-bipartite n-node graph G in O(τ(G)) time and \(O(\tau(G)\sqrt{n}\log^{3/2} n)\) messages, where τ(G) is the mixing time of a random walk on G. The above result implies highly efficient (sublinear running time and messages) leader election algorithms for networks with small mixing times, such as expanders and hypercubes. In contrast, previous leader election algorithms had at least linear message complexity even in complete graphs. Moreover, super-linear message lower bounds are known for time-efficient deterministic leader election algorithms. Finally, an almost-tight lower bound is presented for randomized leader election, showing that \(\Omega(\sqrt n)\) messages are needed for any O(1) time leader election algorithm which succeeds with high probability. It is also shown that Ω(n 1/3) messages are needed by any leader election algorithm that succeeds with high probability, regardless of the number of the rounds. We view our results as a step towards understanding the randomized complexity of leader election in distributed networks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Afek, Y., Gafni, E.: Time and message bounds for election in synchronous and asynchronous complete networks. SICOMP 20(2), 376–394 (1991)
Afek, Y., Matias, Y.: Elections in anonymous networks. Inf. Comput. 113(2), 312–330 (1994)
Angluin, D.: Local and global properties in networks of processors (extended abstract). In: STOC, pp. 82–93 (1980)
Augustine, J., Pandurangan, G., Robinson, P., Upfal, E.: Towards robust and efficient distributed computation in dynamic peer-to-peer networks. In: SODA (2012)
Snir, M., Scheiber, B.: Calling names on nameless networks. Inf. Comput. 113(1), 80–101 (1994)
Loui, M.C., Matsushita, T.A., West, D.B.: Election in a complete network with a sense of direction. Information Processing Letters 22(4), 185–187 (1986)
Chandra, T.D., Griesemer, R., Redstone, J.: Paxos made live - an engineering perspective (2006 invited talk). In: Proceedings of the 26th Annual ACM Symposium on Principles of Distributed Computing (2007)
Gallager, R.G., Humblet, P.A., Spira, P.M.: A distributed algorithm for minimum-weight spanning trees. ACM Trans. Program. Lang. Syst. 5(1), 66–77 (1983)
Gupta, I., van Renesse, R., Birman, K.P.: A Probabilistically Correct Leader Election Protocol for Large Groups. In: Herlihy, M.P. (ed.) DISC 2000. LNCS, vol. 1914, pp. 89–103. Springer, Heidelberg (2000)
Humblet, P.: Electing a leader in a clique in O(n logn) messages. Intern. Memo., Laboratory for Information and Decision Systems. M.I.T, Cambridge (1984)
Itai, A., Rodeh, M.: Symmetry breaking in distributed networks. Inf. Comput. 88(1), 60–87 (1990)
Khan, M., Kuhn, F., Malkhi, D., Pandurangan, G., Talwar, K.: Efficient distributed approximation algorithms via probabilistic tree embeddings. In: Proceedings of the Twenty-Seventh ACM Symposium on Principles of Distributed Computing, PODC 2008, pp. 263–272. ACM, New York (2008)
Korach, E., Kutten, S., Moran, S.: A modular technique for the design of efficient distributed leader finding algorithms. ACM Trans. Program. Lang. Syst. 12(1), 84–101 (1990)
Korach, E., Moran, S., Zaks, S.: Tight lower and upper bounds for some distributed algorithms for a complete network of processors. In: PODC 1984, pp. 199–207. ACM, New York (1984)
Korach, E., Moran, S., Zaks, S.: The optimality of distributive constructions of minimum weight and degree restricted spanning trees in a complete network of processors. SIAM Journal on Computing 16(2), 231–236 (1987)
Korach, E., Moran, S., Zaks, S.: Optimal lower bounds for some distributed algorithms for a complete network of processors. Theoretical Computer Science 64(1), 125–132 (1989)
Lamport, L.: Time, clocks, and the ordering of events in a distributed system. Commun. ACM 21(7), 558–565 (1978)
Lamport, L.: The part-time parliament. ACM Trans. Comput. Syst. 16(2), 133–169 (1998)
Le Lann, G.: Distributed systems - towards a formal approach. In: IFIP Congress, pp. 155–160 (1977)
Lynch, N.: Distributed Algorithms. Morgan Kaufman Publishers, Inc., San Francisco (1996)
Malkhi, D., Reiter, M., Wright, R.: Probabilistic quorum systems. In: PODC 1997, pp. 267–273. ACM, New York (1997)
Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press (2004)
Nygren, E., Sitaraman, R.K., Sun, J.: The akamai network: a platform for high-performance internet applications. SIGOPS Oper. Syst. Rev. 44(3), 2–19 (2010)
Peleg, D.: Time-optimal leader election in general networks. Journal of Parallel and Distributed Computing 8(1), 96–99 (1990)
Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM (2000)
Ramanathan, M.K., Ferreira, R.A., Jagannathan, S., Grama, A., Szpankowski, W.: Randomized leader election. Distributed Computing, 403–418 (2007)
Ratnasamy, S., Francis, P., Handley, M., Karp, R., Shenker, S.: A scalable content-addressable network. In: SIGCOMM 2001, pp. 161–172. ACM, New York (2001)
Rowstron, A., Druschel, P.: Pastry: Scalable, Decentralized Object Location, and Routing for Large-Scale Peer-to-Peer Systems. In: Guerraoui, R. (ed.) Middleware 2001. LNCS, vol. 2218, pp. 329–350. Springer, Heidelberg (2001)
Santoro, N.: Design and Analysis of Distributed Algorithms. Wiley Series on Parallel and Distributed Computing. Wiley-Interscience (2006)
Singh, G.: Efficient distributed algorithms for leader election in complete networks. In: ICDCS, pp. 472–479 (1991)
Tel, G.: Introduction to distributed algorithms. Cambridge University Press, New York (1994)
Zhao, B.Y., Huang, L., Stribling, J., Rhea, S.C., Joseph, A.D., Kubiatowicz, J.D.: Tapestry: a resilient global-scale overlay for service deployment. IEEE Journal on Selected Areas in Communications 22(1), 41–53 (2004)
Kutten, S., Zinenko, D.: Low Communication Self-stabilization through Randomization. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 465–479. Springer, Heidelberg (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kutten, S., Pandurangan, G., Peleg, D., Robinson, P., Trehan, A. (2013). Sublinear Bounds for Randomized Leader Election. In: Frey, D., Raynal, M., Sarkar, S., Shyamasundar, R.K., Sinha, P. (eds) Distributed Computing and Networking. ICDCN 2013. Lecture Notes in Computer Science, vol 7730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35668-1_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-35668-1_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35667-4
Online ISBN: 978-3-642-35668-1
eBook Packages: Computer ScienceComputer Science (R0)