Abstract.
We investigate issues related to the probe complexity of quorum systems and their implementation in a dynamic environment. Our contribution is twofold. The first regards the algorithmic complexity of finding a quorum in case of random failures. We show a tradeoff between the load of a quorum system and its probe complexity for non adaptive algorithms. We analyze the algorithmic probe complexity of the Paths quorum system suggested by Naor and Wool in [29], and present two optimal algorithms. The first is a non adaptive algorithm that matches our lower bound. The second is an adaptive algorithm with a probe complexity that is linear in the cardinality of the smallest quorum set. We supply a constant degree network in which these algorithms could be executed efficiently. Thus the Paths quorum system is shown to have good balance between many measures of quality. Our second contribution is presenting Dynamic Paths - a suggestion for a dynamic and scalable quorum system, which can operate in an environment where elements join and leave the system. The quorum system could be viewed as a dynamic adaptation of the Paths system, and therefore has low load high availability and good probe complexity. We show that it scales gracefully as the number of elements grows.
Similar content being viewed by others
References
El Abbadi A, Skeen D, Cristian F: An efficient, fault-tolerant protocal for replicated data management. In: Proceedings of the 5th ACM SIGACT/SIGMOD Conference on Principles of Database Systems, 1985, pp 215-229
Abraham I, Awerbuch B, Azar Y, Bartal Y, Malkhi D, Pavlov E: A generic scheme for building overlay networks in adversarial scenarios. In: Proceedings of the International Parallel and Distributed Processing Symposium (IPDPS), 2003, p 40
Abraham I, Malkhi D: Probabilistic quorums for dynamic systmes. In: Proceedings of the 17th International Symposium on Distributed Computing (DISC), 2003, pp 60-74
Adler M, Halperin E, Karp RM, Vazirani VV: A stochastic process on the hypercube with applications to peer-to-peer networks. In: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing (STOC), 2003, pp 575-584
Agrawal D, Egecioglu O, El Abbadi A: Billiard quorums on the grid. Information Processing Letters 64(1):9-16 (1997)
Aizenman M, Chayes J, Chayes L, Frohlich J, Russo L: On a sharp transition from area low to perimeter low in a system of random surfaces. Commun Math Phys 92:19-69, 1983.
Bazzi RA: Planar quorums. In: Distributed Algorithms, 10th International Workshop, WDAG ‘96, pp 251-268
Bearden M, Bianchini RP Jr: A fault-tolerant algorithm for decentralized on-line quorum adaptation. In: Symposium on Fault-Tolerant Computing, 1998, pp 262-271
Bollobas B, Riordan O: The critical probability for random voronoi percolation in the plane is 1/2. In: Front for the Mathematics ArXiv, math.PR/0410336, 14 October 2004
Garcia-Molina H, Barbara D: How to assign votes in a distributed system. J Assoc Comput Mach 32(4):841-855 (1985)
Goldreich O: Randomized Methods in Computation - Lecture Notes. http://www.wisdom.weizmann.ac.il/~oded/rnd.html, 2001
Grimmett G: Percolation, 2nd ed. Springer-Verlag, 1999
Haas ZJ, Liang B: Ad hoc mobility management with uniform quorum systems. IEEE/ACM Trans Network 7(2):228-240 (1999)
Hassin Y, Peleg D: Average probe complexity in quorum systems. In: 20th ACM Symposium on Principles of Distributed Computing (PODC), 2001, pp 180-189
Herlihy M: Dynamic quorum adjustment for partitioned data. ACM Trans Database Syst (TODS) 12:170-194 (1987)
Jajodia S. Mutchler D: Dynamic voting algorithms for maintaining the consistency of a replicated database. ACM Trans Database Syst 15(2):230-280 (1990)
Karumanchi G, Muralidharan S, Prakash R: Information dissemination in partitionable mobile ad hoc networks. In: Proceedings of IEEE Symposium on Reliable Distributed Systems, 1999, pp 4-13
Liggett TL, Schonmann RH, Stacey AM: Domination by product measures. The Annals of Probability 25(1):71-95 (1997)
Lotem EY, Keidar I, Dolev D: Dynamic voting for consistent primary components. In: Symposium on Principles of Distributed Computing (PODC), 1997, pp 63-71
Lynch N, Shvartsman A: Robust emulation of shared memory using dynamic quorum-acknowledged broadcasts. In: Symposium on Fault-Tolerant Computing, 1997, pp 272-281
Lynch N, Shvartsman A: Rambo: A reconfigurable atomic memory service for dynamic networks. In: Proceedings of the 16th International Symposium on Distributed Computing, 2002, pp 173-190
Maekawa M: A \(\sqrt{N}\) algorithm for mutual exclusion in decentralized systems. ACM Trans Comput Syst 3(2):145-159 (1985)
Malkhi D, Naor M, Ratajczak D: Viceroy: A scalable and dynamic emulation of the butterfly. In: ACM Conf. on Principles of Distributed Computing (PODC), 2002, pp 183-192
Menshikov MV: Coincidence of critical points in percolation problems. Soviet Mathematics Doklady 33:856-859 (1986)
Motwani R, Raghavan P: Randomized Algorithms. Cambridge University Press, 1997
Nadav U, Naor M: Fault-tolerant storage in a dynamic environment. In: Proceedings of the 18th Annual Conference on Distributed Computing (DISC). Lecture Notes in Computer Science 3274, Springer, 2004, pp 390-404
Naor M, Wieder U: Novel architectures for p2p applications: the continuous-discrete approach. In: Fifteenth ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 2003, pp 50-59
Naor M, Wool A: Access control and signatures via quorum secret sharing. IEEE Trans Parallel Distrib Syst 9(9):909-922 (1998)
Naor M, Wool A: The load, capacity, and availability of quorum systems. SIAM J Comput 27(2):423-447 (1998)
Okabe A, Boots B, Sugihara K, Chiu SN: Spatial Tessellations -- Concepts and Applications of Voronoi Diagrams. Wiley, Chichester, 2nd ed., 2000
Peleg D, Wool A: How to be an efficient snoop, or the probe complexity of quorum systems. SIAM J Discrete Math 15(3):416-433 (2002)
De Prisco R, Fekete A, Lynch N, Shvartsman A: A dynamic view-oriented group communication service. In: Symposium on Principles of Distributed Computing (PODC), 1998, pp 227-236
Ratnasamy S, Francis P, Handley M, Karp R, Shenker S: A scalable content addressable network. In: Proc ACM SIGCOMM, 2001, pp 161-172
Sanders BA: The information structure of distributed mutual exclusion algorithms. ACM Trans Comput Syst 5(3):284-299 (1987)
Stoica I, Morris R, Karger D, Kaashoek F, Balakrishnan H: Chord: A scalable Peer-To-Peer lookup service for internet applications. In: Proceedings of the 2001 ACM SIGCOMM Conference, 2001, pp 149-160
Stojmenović I, Pena PEV: A scalable quorum based location update scheme for routing in ad hoc wireless networks. Technical Report TR-99-09, SITE, University of Ottawa, September 1999
Author information
Authors and Affiliations
Corresponding author
Additional information
Published online: 10 December 2004
Moni Naor: Incumbent of the Judith Kleeman ProfessorialChair.
Research supported in part by the RAND/APX grant from the EU Program IST
Rights and permissions
About this article
Cite this article
Naor, M., Wieder, U. Scalable and dynamic quorum systems. Distrib. Comput. 17, 311–322 (2005). https://doi.org/10.1007/s00446-004-0114-3
Issue Date:
DOI: https://doi.org/10.1007/s00446-004-0114-3