research-article

Stabilizing consensus with the power of two choices

Authors:

Benjamin Doerr,

Leslie Ann Goldberg,

Thomas Sauerwald, and

Christian ScheidelerAuthors Info & Claims

SPAA '11: Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures

June 2011

Pages 149 - 158

https://doi.org/10.1145/1989493.1989516

Published: 04 June 2011 Publication History

Abstract

In the standard consensus problem there are n processes with possibly different input values and the goal is to eventually reach a point at which all processes commit to exactly one of these values. We are studying a slight variant of the consensus problem called the stabilizing consensus problem [2]. In this problem, we do not require that each process commits to a final value at some point, but that eventually they arrive at a common, stable value without necessarily being aware of that. This should work irrespective of the states in which the processes are starting. Our main result is a simple randomized algorithm called median rule that, with high probability, just needs O(log m log log n + log n) time and work per process to arrive at an almost stable consensus for any set of m legal values as long as an adversary can corrupt the states of at most √n processes at any time. Without adversarial involvement, just O(log n) time and work is needed for a stable consensus, with high probability. As a by-product, we obtain a simple distributed algorithm for approximating the median of n numbers in time O(log m log log n + log n) under adversarial presence.

References

[1]

D. Angluin, J. Aspnes, and D. Eisenstat. A simple population protocol for fast robust approximate majority. In Proc. of the 21st Int. Symposium on Distributed Computing (DISC), pages 20--32, 2007.

Digital Library

[2]

D. Angluin, M. Fischer, and H. Jiang. Stabilizing consensus in mobile networks. In Proc. of the Intl. Conference on Distributed Computing in Sensor Networks (DCOSS), pages 37--50, 2006.

Digital Library

[3]

J. Aspnes. Randomized protocols for aynchronous consensus. Distributed Computing, 16(2-3):165--176, 2003.

Digital Library

[4]

J. Aspnes, H. Attiya, and K. Censor. Randomized consensus in expected o(n łog n) individual work. In Proc. of the 27th ACM Symp. on Principles of Distributed Computing (PODC), pages 325--333, 2008.

Digital Library

[5]

J. Aspnes and K. Censor. Approximate shared-memory counting despite a strong adversary. In Proc. of the 20th ACM Symp. on Discrete Algorithms (SODA), pages 441--450, 2009.

Digital Library

[6]

H. Attiya and K. Censor. Lower bounds for randomized consensus under a weak adversary. In Proc. of the 27th ACM Symp. on Principles of Distributed Computing (PODC), pages 315--324, 2008.

Digital Library

[7]

H. Attiya and K. Censor. Tight bounds for asynchronous randomized consensus. Journal of the ACM, 55(5):1--26, 2008.

Digital Library

[8]

H. Attiya and J. Welch. Distributed Computing: Fundamentals, Simulations, and Advanced Topics (2nd Edition). John Wiley and Sons, 2004.

Digital Library

[9]

Y. Azar, A. Broder, A. Karlin, and E. Upfal. Balanced allocations. SIAM Journal on Computing, 29(1):180--200, 1999.

Digital Library

[10]

Z. Bar Joseph and M. Ben-Or. A tight lower bound for randomized synchronous consensus. In Proc. of the 17th ACM Symp. on Principles of Distributed Computing (PODC), pages 193--199, 1998.

Digital Library

[11]

M. Ben-Or, E. Pavlov, and V. Vaikuntanathan. Byzantine agreement in the full-information model in O(łog n) rounds. In Proc. of the 38th ACM Symp. on Theory of Computing (STOC), pages 179--186, 2006.

Digital Library

[12]

R. Canetti and T. Rabin. Fast asynchronous Byzantine agreement with optimal resilience. In Proc. of the 25th ACM Symp. on Theory of Computing (STOC), pages 42--51, 1993.

Digital Library

[13]

R. Cole, A. Frieze, B.M. Maggs, M. Mitzenmacher, A.W. Richa, R.K. Sitaraman, and E. Upfal. On balls and bins with deletions. In Proc. of the 2nd Intl. Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM), 1998.

Digital Library

[14]

R. Cole, B.M. Maggs, F. Meyer auf der Heide, M. Mitzenmacher, A.W. Richa, K. Schröder, R.K. Sitaraman, and B. Vöcking. Randomized protocols for low-congestion circuit routing in multistage interconnection networks. In Proc. of the 29th ACM Symp. on Theory of Computing (STOC), pages 378--388, 1998.

Digital Library

[15]

M. Dietzfelbinger and F. Meyer auf der Heide. Simple, efficient shared memory simulations. In Proc. of the 10th ACM Symp. on Parallel Algorithms and Architectures (SPAA), pages 110--119, 1993.

Digital Library

[16]

D. Dolev, N. Lynch, S. Pinter, E. Stark, and W. Weihl. Reaching approximate agreement in the presence of faults. Journal of the ACM, 33(3):499--516, 1986.

Digital Library

[17]

S. Dolev, R. Kat, and E. Schiller. When consensus meets self-stabilization. In Proc. of the 10th International Conference on Principle of Distributed Systems (OPODIS), pages 45--63, 2006.

Digital Library

[18]

R. Elsasser and T. Sauerwald. The power of memory in randomized broadcasting. In Proc. of the 19th ACM Symp. on Discrete Algorithms (SODA), pages 773--781, 2008.

Digital Library

[19]

P. Feldman and S. Micali. An optimal probabilistic protocol for synchronous Byzantine agreement. SIAM Journal on Computing, 26(4):873--933, 1997.

Digital Library

[20]

M. Fischer, N. Lynch, and M. Merritt. Easy impossibility proofs for distributed consensus problems. Distributed Computing, 1(1):26--39, 1986.

Digital Library

[21]

M. Fischer, N. Lynch, and M. Paterson. Impossibility of distributed consensus with one faulty process. Journal of the ACM, 32(2):374--382, 1985.

Digital Library

[22]

S. Gilbert and D. Kowalski. Distributed agreement with optimal communication complexity. In Proc. of the 21st ACM Symp. on Discrete Algorithms (SODA), pages 965--977, 2010.

Digital Library

[23]

K. Ito and H.P. McKean. Diffusion Processes and their Sample Paths. Springer Verlag, Heidelberg, 1974.

[24]

N.L. Johnson and S. Kotz. Encyclopedia of Statistical Sciences. John Wiley, New York, 1982.

[25]

B. Kapron, D. Kempe, V. King, J. Saia, and V. Sanwalani. Fast asynchronous Byzantine agreement and leader election with full information. In Proc. of the 19th ACM Symp. on Discrete Algorithms (SODA), pages 1038--1047, 2008.

Digital Library

[26]

R. Karp, M. Luby, and F. Meyer auf der Heide. Efficient PRAM simulation on a distributed memory machine. In Proc. of the 24th ACM Symp. on Theory of Computing (STOC), pages 318--326, 1992.

Digital Library

[27]

J. Katz and C.-Y. Koo. On expected constant-round protocols for Byzantine agreement. Journal of Computer and System Sciences, 75(2):91--112, 2009.

Digital Library

[28]

D. Kempe, A. Dobra, and J. Gehrke. Gossip-based computation of aggregate information. In Proc. of the 44 IEEE Symp. on Foundations of Computer Science (FOCS), pages 482--491, 2003.

Digital Library

[29]

V. King and J. Saia. Breaking the O(n<sup>2</sup>) bit barrier: Scalable Byzantine agreement with an adaptive adversary. In Proc. of the 29th ACM Symp. on Principles of Distributed Computing (PODC), pages 420--429, 2010.

Digital Library

[30]

V. King, J. Saia, V. Sanwalani, and E. Vee. Towards secure and scalable computation in peer-to-peer networks. In Proc. of the 47th IEEE Symp. on Foundations of Computer Science (FOCS), pages 87--98, 2006.

Digital Library

[31]

F. Kuhn, T. Locher, and R. Wattenhofer. Tight bounds for distributed selection. In Proc. of the 19th ACM Symp. on Parallel Algorithms and Architectures (SPAA), pages 145--153, 2007.

Digital Library

[32]

N. Lynch. Distributed Algorithms. Morgan Kaufmann Publishers, 1996.

Digital Library

[33]

B. Patt-Shamir. A note on efficient aggregate queries in sensor networks. Theoretical Computer Science, 370(1-3):254--264, 2007.

Digital Library

[34]

M. Rabin. Randomized Byzantine generals. In Proc. of the 24th IEEE Symp. on Foundations of Computer Science (FOCS), pages 403--409, 1983.

Digital Library

[35]

N. Shrivastava, C. Buragohain, D. Agrawal, and S. Suri. Medians and beyond: new aggregation techniques for sensor networks. In Proc. of the 2nd Intl. Conference on Embedded Networked Sensor Systems (SenSys), pages 239--249, 2004.

Digital Library

Cited By

Dou JScheideler CGramoli V(2024)Invited Paper: Blockchains made Lightweight: A Median Rule for State Machine ReplicationProceedings of the 2024 Workshop on Advanced Tools, Programming Languages, and PLatforms for Implementing and Evaluating algorithms for Distributed systems10.1145/3663338.3665452(1-5)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3663338.3665452
Korman AVacus R(2024)Early adapting to trends: self-stabilizing information spread using passive communicationDistributed Computing10.1007/s00446-024-00462-8Online publication date: 22-Feb-2024
https://doi.org/10.1007/s00446-024-00462-8
Amores-Sesar ICachin CSchneider P(2024)An Analysis of Avalanche ConsensusStructural Information and Communication Complexity10.1007/978-3-031-60603-8_2(27-44)Online publication date: 27-May-2024
https://dl.acm.org/doi/10.1007/978-3-031-60603-8_2
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Index Terms

Stabilizing consensus with the power of two choices
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

SPAA '11: Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures

June 2011

404 pages

ISBN:9781450307437

DOI:10.1145/1989493

Co-chairs:
Friedhelm Meyer auf der Heide
University of Paderborn, Germany
,
Rajmohan Rajaraman
Northeastern University, USA

Copyright © 2011 ACM.

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Published: 04 June 2011

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SPAA '11: 23rd ACM Symposium on Parallelism in Algorithms and Architectures

June 4 - 6, 2011

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https://dl.acm.org/doi/10.1145/3663338.3665452
Korman AVacus R(2024)Early adapting to trends: self-stabilizing information spread using passive communicationDistributed Computing10.1007/s00446-024-00462-8Online publication date: 22-Feb-2024
https://doi.org/10.1007/s00446-024-00462-8
Amores-Sesar ICachin CSchneider P(2024)An Analysis of Avalanche ConsensusStructural Information and Communication Complexity10.1007/978-3-031-60603-8_2(27-44)Online publication date: 27-May-2024
https://dl.acm.org/doi/10.1007/978-3-031-60603-8_2
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