Article

Local Algorithms: Self-stabilization on Speed

Authors:

Christoph Lenzen,

Jukka Suomela, and

Roger WattenhoferAuthors Info & Claims

SSS '09: Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems

November 2009

Pages 17 - 34

https://doi.org/10.1007/978-3-642-05118-0_2

Published: 05 November 2009 Publication History

Abstract

Fault tolerance is one of the main concepts in distributed computing. It has been tackled from different angles, e.g. by building replicated systems that can survive crash failures of individual components, or even systems that can tolerate a minority of arbitrarily malicious ("Byzantine") participants.

Self-stabilization, a fault tolerance concept coined by the late Edsger W. Dijkstra in 1973 [1,2], is of a different stamp. A self-stabilizing system must survive arbitrary failures, beyond Byzantine failures, including for instance a total wipe out of volatile memory at all nodes. In other words, the system must self-heal and converge to a correct state even if starting in an arbitrary state, provided that no further faults happen.

References

[1]

Dijkstra, E.W.: Self-stabilization in spite of distributed control. Manuscript EWD391 (October 1973).

[2]

Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Communications of the ACM 17(11), 643-644 (1974).

Digital Library

[3]

Luby, M.: A simple parallel algorithm for the maximal independent set problem. SIAM Journal on Computing 15(4), 1036-1053 (1986).

Digital Library

[4]

Cole, R., Vishkin, U.: Deterministic coin tossing with applications to optimal parallel list ranking. Information and Control 70(1), 32-53 (1986).

Digital Library

[5]

Linial, N.: Locality in distributed graph algorithms. SIAM Journal on Computing 21(1), 193-201 (1992).

Digital Library

[6]

Naor, M., Stockmeyer, L.: What can be computed locally? SIAM Journal on Computing 24(6), 1259-1277 (1995).

Digital Library

[7]

Suomela, J.: Optimisation Problems inWireless Sensor Networks: Local Algorithms and Local Graphs. PhD thesis, University of Helsinki, Department of Computer Science, Helsinki, Finland (May 2009).

[8]

Awerbuch, B., Sipser, M.: Dynamic networks are as fast as static networks. In: Proc. 29th Symposium on Foundations of Computer Science (FOCS), pp. 206- 219. IEEE, Los Alamitos (1988).

Digital Library

[9]

Awerbuch, B., Varghese, G.: Distributed program checking: a paradigm for building self-stabilizing distributed protocols. In: Proc. 32nd Symposium on Foundations of Computer Science (FOCS), pp. 258-267. IEEE, Los Alamitos (1991).

Digital Library

[10]

Awerbuch, B.: Complexity of network synchronization. Journal of the ACM 32(4), 804-823 (1985).

Digital Library

[11]

Suomela, J.: Survey of local algorithms (manuscript, 2009).

[12]

Goldberg, A.V., Plotkin, S.A.: Parallel (Δ+1)-coloring of constant-degree graphs. Information Processing Letters 25(4), 241-245 (1987).

Digital Library

[13]

Peleg, D.: Distributed Computing - A Locality-Sensitive Approach. SIAM, Philadelphia (2000).

Digital Library

[14]

Schneider, J., Wattenhofer, R.: A log-star distributed maximal independent set algorithm for growth-bounded graphs. In: Proc. 27th Symposium on Principles of Distributed Computing (PODC), pp. 35-44. ACM Press, New York (2008).

Digital Library

[15]

Schneider, M.: Self-stabilization. ACM Computing Surveys 25(1), 45-67 (1993).

Digital Library

[16]

Dolev, S.: Self-Stabilization. The MIT Press, Cambridge (2000).

Digital Library

[17]

Kothapalli, K., Scheideler, C., Onus, M., Schindelhauer, C.: Distributed coloring in Õ(√log n) bit rounds. In: Proc. 20th International Parallel and Distributed Processing Symposium (IPDPS). IEEE, Los Alamitos (2006).

Digital Library

[18]

Awerbuch, B., Patt-Shamir, B., Varghese, G.: Self-stabilization by local checking and correction. In: Proc. 32nd Symposium on Foundations of Computer Science (FOCS), pp. 268-277. IEEE, Los Alamitos (1991).

Digital Library

[19]

Mayer, A., Naor, M., Stockmeryer, L.: Local computations on static and dynamic graphs. In: Proc. 3rd Israel Symposium on the Theory of Computing and Systems (ISTCS), pp. 268-278. IEEE, Los Alamitos (1995).

Digital Library

[20]

Awerbuch, B., Kutten, S., Mansour, Y., Patt-Shamir, B., Varghese, G.: Time optimal self-stabilizing synchronization. In: Proc. 25th Symposium on Theory of Computing (STOC), pp. 652-661. ACM Press, New York (1993).

Digital Library

[21]

Angluin, D.: Local and global properties in networks of processors. In: Proc. 12th Symposium on Theory of Computing (STOC), pp. 82-93. ACM Press, New York (1980).

Digital Library

[22]

Goldberg, A.V., Plotkin, S.A., Shannon, G.E.: Parallel symmetry-breaking in sparse graphs. SIAM Journal on Discrete Mathematics 1(4), 434-446 (1988).

Digital Library

[23]

Kuhn, F., Wattenhofer, R.: On the complexity of distributed graph coloring. In: Proc. 25th Symposium on Principles of Distributed Computing (PODC), pp. 7-15. ACM Press, New York (2006).

Digital Library

[24]

Barenboim, L., Elkin, M.: Distributed (Δ+ 1)-coloring in linear (in Δ) time. In: Proc. 41st Symposium on Theory of Computing (STOC), pp. 111-120. ACM Press, New York (2009).

Digital Library

[25]

Kuhn, F.: Weak graph colorings: Distributed algorithms and applications. In: Proc. 21st Symposium on Parallelism in Algorithms and Architectures (SPAA). ACM Press, New York (to appear, 2009).

Digital Library

[26]

Panconesi, A., Rizzi, R.: Some simple distributed algorithms for sparse networks. Distributed Computing 14(2), 97-100 (2001).

Digital Library

[27]

Hańćkowiak, M., Karoński, M., Panconesi, A.: On the distributed complexity of computing maximal matchings. SIAM Journal on Discrete Mathematics 15(1), 41- 57 (2001).

Digital Library

[28]

Alon, N., Babai, L., Itai, A.: A fast and simple randomized parallel algorithm for the maximal independent set problem. Journal of Algorithms 7(4), 567-583 (1986).

Digital Library

[29]

Israeli, A., Itai, A.: A fast and simple randomized parallel algorithm for maximal matching. Information Processing Letters 22(2), 77-80 (1986).

Digital Library

[30]

Métivier, Y., Robson, J.M., Nasser, S.D., Zemmari, A.: An optimal bit complexity randomised distributed MIS algorithm. In: SIROCCO 2009. LNCS, vol. 5869. Springer, Heidelberg (to appear, 2009).

[31]

Kutten, S., Peleg, D.: Tight fault locality. SIAM Journal on Computing 30(1), 247-268 (2000).

Digital Library

[32]

Papadimitriou, C.H., Yannakakis, M.: Linear programming without the matrix. In: Proc. 25th Symposium on Theory of Computing (STOC), pp. 121-129. ACM Press, New York (1993).

Digital Library

[33]

Bartal, Y., Byers, J.W., Raz, D.: Global optimization using local information with applications to flow control. In: Proc. 38th Symposium on Foundations of Computer Science (FOCS), pp. 303-312. IEEE Computer Society Press, Los Alamitos (1997).

Digital Library

[34]

Kuhn, F., Wattenhofer, R.: Constant-time distributed dominating set approximation. Distributed Computing 17(4), 303-310 (2005).

Digital Library

[35]

Kuhn, F., Moscibroda, T., Wattenhofer, R.: The price of being near-sighted. In: Proc. 17th Symposium on Discrete Algorithms (SODA), pp. 980-989. ACM Press, New York (2006).

Digital Library

[36]

Kuhn, F., Moscibroda, T., Wattenhofer, R.: What cannot be computed locally! In: Proc. 23rd Symposium on Principles of Distributed Computing (PODC), pp. 300-309. ACM Press, New York (2004).

Digital Library

[37]

Floréen, P., Kaasinen, J., Kaski, P., Suomela, J.: An optimal local approximation algorithm for max-min linear programs. In: Proc. 21st Symposium on Parallelism in Algorithms and Architectures (SPAA). ACM Press, New York (to appear, 2009).

Digital Library

[38]

Floréen, P., Hassinen, M., Kaski, P., Suomela, J.: Tight local approximation results for max-min linear programs. In: Fekete, S.P. (ed.) ALGOSENSORS 2008. LNCS, vol. 5389, pp. 2-17. Springer, Heidelberg (2008).

Digital Library

[39]

Floréen, P., Kaski, P., Musto, T., Suomela, J.: Approximating max-min linear programs with local algorithms. In: Proc. 22nd International Parallel and Distributed Processing Symposium (IPDPS). IEEE, Los Alamitos (2008).

[40]

Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover Publications, Inc., Mineola (1998).

Digital Library

[41]

Vazirani, V.V.: Approximation Algorithms. Springer, Heidelberg (2001).

Digital Library

[42]

Kuhn, F., Moscibroda, T., Wattenhofer, R.: Fault-tolerant clustering in ad hoc and sensor networks. In: Proc. 26th International Conference on Distributed Computing Systems (ICDCS). IEEE Computer Society Press, Los Alamitos (2006).

Digital Library

[43]

Hochbaum, D.S.: Approximation algorithms for the set covering and vertex cover problems. SIAM Journal on Computing 11(3), 555-556 (1982).

[44]

Åstrand, M., Floréen, P., Polishchuk, V., Rybicki, J., Suomela, J., Uitto, J.: A local 2-approximation algorithm for the vertex cover problem. In: Proc. 23rd Symposium on Distributed Computing (DISC). Springer, Heidelberg (to appear, 2009).

Digital Library

[45]

Czygrinow, A., Hańćkowiak, M., Wawrzyniak,W.: Fast distributed approximations in planar graphs. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 78-92. Springer, Heidelberg (2008).

Digital Library

[46]

Lenzen, C., Wattenhofer, R.: Leveraging Linial's locality limit. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 394-407. Springer, Heidelberg (2008).

Digital Library

[47]

Lenzen, C., Oswald, Y.A., Wattenhofer, R.: What can be approximated locally? In: Proc. 20th Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 46-54. ACM Press, New York (2008).

Digital Library

[48]

Elkin, M.: Distributed approximation: a survey. ACM SIGACT News 35(4), 40-57 (2004).

Digital Library

[49]

Sterling, A.: Self-assembling systems are distributed systems. Manuscript, arXiv:0907.1072 {cs.DC} (July 2009).

Cited By

Johnen CDevismes SMazoit FIlcinkas DKuznetsov PGelles ROlivetti D(2024)Asynchronous Self-stabilization Made Fast, Simple, and Energy-efficientProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662803(538-548)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662803
Fu XYin YZheng C(2023)Self-stabilizing -Coloring in Sublinear (in ) Rounds via Locally-Iterative AlgorithmsComputing and Combinatorics10.1007/978-3-031-49190-0_17(232-243)Online publication date: 15-Dec-2023
https://dl.acm.org/doi/10.1007/978-3-031-49190-0_17
Balliu AHirvonen JMelnyk DOlivetti DRybicki JSuomela J(2022)Local MendingStructural Information and Communication Complexity10.1007/978-3-031-09993-9_1(1-20)Online publication date: 27-Jun-2022
https://dl.acm.org/doi/10.1007/978-3-031-09993-9_1
Show More Cited By

Index Terms

Local Algorithms: Self-stabilization on Speed
1. Computer systems organization
  1. Architectures
    1. Distributed architectures
  2. Dependable and fault-tolerant systems and networks
2. Software and its engineering
  1. Software organization and properties
    1. Software system structures
      1. Distributed systems organizing principles

Index terms have been assigned to the content through auto-classification.

Recommendations

Increasing System Availability with Local Recovery Based on Fault Localization
QSIC '10: Proceedings of the 2010 10th International Conference on Quality Software

Due to the fact that software systems cannot be tested exhaustively, software systems must cope with residual defects at run-time. Local recovery is an approach for recovering from errors, in which only the defective parts of the system are recovered ...
Read More
The design of fault-tolerant parallel algorithms
Read More
Resilience of mutual exclusion algorithms to transient memory faults
PODC '11: Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing

We study the behavior of mutual exclusion algorithms in the presence of unreliable shared memory subject to transient memory faults. It is well-known that classical 2-process mutual exclusion algorithms, such as Dekker and Peterson's algorithms, are not ...
Read More

Comments

Information & Contributors

Information

Published In

cover image Guide Proceedings

SSS '09: Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems

November 2009

798 pages

ISBN:9783642051173

Editors:
Rachid Guerraoui
Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland CH 1015
,
Franck Petit
LIP, ENS Lyon, Lyon cedex 07, France 69236

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 05 November 2009

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

18
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Other Metrics

View Author Metrics

Citations

Cited By

Johnen CDevismes SMazoit FIlcinkas DKuznetsov PGelles ROlivetti D(2024)Asynchronous Self-stabilization Made Fast, Simple, and Energy-efficientProceedings of the 43rd ACM Symposium on Principles of Distributed Computing10.1145/3662158.3662803(538-548)Online publication date: 17-Jun-2024
https://dl.acm.org/doi/10.1145/3662158.3662803
Fu XYin YZheng C(2023)Self-stabilizing -Coloring in Sublinear (in ) Rounds via Locally-Iterative AlgorithmsComputing and Combinatorics10.1007/978-3-031-49190-0_17(232-243)Online publication date: 15-Dec-2023
https://dl.acm.org/doi/10.1007/978-3-031-49190-0_17
Balliu AHirvonen JMelnyk DOlivetti DRybicki JSuomela J(2022)Local MendingStructural Information and Communication Complexity10.1007/978-3-031-09993-9_1(1-20)Online publication date: 27-Jun-2022
https://dl.acm.org/doi/10.1007/978-3-031-09993-9_1
Barenboim LElkin MGoldenberg U(2021)Locally-iterative Distributed (Δ + 1)-coloring and ApplicationsJournal of the ACM10.1145/348662569:1(1-26)Online publication date: 7-Dec-2021
https://dl.acm.org/doi/10.1145/3486625
Feldmann MScheideler CSchmid S(2020)Survey on Algorithms for Self-stabilizing Overlay NetworksACM Computing Surveys10.1145/339719053:4(1-24)Online publication date: 11-Jul-2020
https://dl.acm.org/doi/10.1145/3397190
Turau V(2019)Making Randomized Algorithms Self-stabilizingStructural Information and Communication Complexity10.1007/978-3-030-24922-9_21(309-324)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1007/978-3-030-24922-9_21
Censor-Hillel KHaramaty EKarnin ZGiakkoupis G(2016)Optimal Dynamic Distributed MISProceedings of the 2016 ACM Symposium on Principles of Distributed Computing10.1145/2933057.2933083(217-226)Online publication date: 25-Jul-2016
https://dl.acm.org/doi/10.1145/2933057.2933083
Kuhn FMoscibroda TWattenhofer R(2016)Local ComputationJournal of the ACM10.1145/274201263:2(1-44)Online publication date: 31-Mar-2016
https://dl.acm.org/doi/10.1145/2742012
Kamei SIzumi TYamauchi Y(2016)An asynchronous self-stabilizing approximation for the minimum CDS with safe convergence in UDGsTheoretical Computer Science10.1016/j.tcs.2015.12.001615:C(102-119)Online publication date: 15-Feb-2016
https://dl.acm.org/doi/10.1016/j.tcs.2015.12.001
Jacob RRicha AScheideler CSchmid STäubig H(2014)SKIP+Journal of the ACM10.1145/262969561:6(1-26)Online publication date: 17-Dec-2014
https://dl.acm.org/doi/10.1145/2629695
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Table of Contents