research-article

Silent self-stabilizing scheme for spanning-tree-like constructions

Authors:

Stéphane Devismes,

David Ilcinkas, and

Colette JohnenAuthors Info & Claims

ICDCN '19: Proceedings of the 20th International Conference on Distributed Computing and Networking

January 2019

Pages 158 - 167

https://doi.org/10.1145/3288599.3288607

Published: 04 January 2019 Publication History

Abstract

In this paper, we propose a general scheme, called Algorithm STIC, to compute spanning-tree-like data structures on arbitrary networks. STIC is self-stabilizing and silent and, despite its generality, is also efficient. It is written in the locally shared memory model with composite atomicity assuming the distributed unfair daemon, the weakest scheduling assumption of the model.

Its stabilization time is in O(n_maxCC) rounds, where n_maxCC is the maximum number of processes in a connected component. We also exhibit polynomial upper bounds on its stabilization time in steps and process moves holding for large classes of instantiations of Algorithm STIC.

We illustrate the versatility of our approach by proposing several such instantiations that efficiently solve classical problems such as leader election, as well as, unconstrained and shortest-path spanning tree constructions.

References

[1]

Y. Afek and G. M. Brown. 1993. Self-Stabilization Over Unreliable Communication Media. Distributed Computing 7, 1 (1993), 27--34.

Digital Library

[2]

K. Altisen, A. Cournier, S. Devismes, A. Durand, and F. Petit. 2017. Self-stabilizing Leader Election in Polynomial Steps. Information and Computation 254 (2017), 330--366.

[3]

Anish Arora, Mohamed G. Gouda, and Ted Herman. 1990. Composite Routing Protocols. In Proceedings of the Second IEEE Symposium on Parallel and Distributed Processing, SPDP 1990. IEEE Computer Society, Dallas, Texas, USA, 70--78.

Digital Library

[4]

Joffroy Beauquier, Maria Gradinariu, and Colette Johnen. 2001. Cross-Over Composition - Enforcement of Fairness under Unfair Adversary. In Self-Stabilizing Systems, 5th International Workshop, WSS 2001 (Lecture Notes in Computer Science), Ajoy Kumar Datta and Ted Herman (Eds.), Vol. 2194. Springer, Lisbon, Portugal, 19--34.

Digital Library

[5]

Lélia Blin, Alain Cournier, and Vincent Villain. 2003. An Improved Snap-Stabilizing PIF Algorithm. In Self-Stabilizing Systems, 6th International Symposium, SSS 2003 (Lecture Notes in Computer Science), Shing-Tsaan Huang and Ted Herman (Eds.), Vol. 2704. Springer, San Francisco, CA, USA, 199--214.

Digital Library

[6]

Lélia Blin, Pierre Fraigniaud, and Boaz Patt-Shamir. 2014. On Proof-Labeling Schemes versus Silent Self-stabilizing Algorithms. In Stabilization, Safety, and Security of Distributed Systems - 16th International Symposium, SSS 2014 (Lecture Notes in Computer Science), Pascal Felber and Vijay K. Garg (Eds.), Vol. 8756. Springer, Paderborn, Germany, 18--32.

[7]

Lélia Blin, Maria Gradinariu Potop-Butucaru, Stephane Rovedakis, and Sébastien Tixeuil. 2010. Loop-Free Super-Stabilizing Spanning Tree Construction. In Stabilization, Safety, and Security of Distributed Systems - 12th International Symposium, SSS 2010 (Lecture Notes in Computer Science), Shlomi Dolev, Jorge Arturo Cobb, Michael J. Fischer, and Moti Yung (Eds.), Vol. 6366. Springer, New York, NY, USA, 50--64.

Digital Library

[8]

Fabienne Carrier, Ajoy Kumar Datta, Stéphane Devismes, Lawrence L. Larmore, and Yvan Rivierre. 2015. Self-stabilizing (f, g)-alliances with safe convergence. J. Parallel and Distrib. Comput. 81--82 (2015), 11--23.

Digital Library

[9]

Jorge Arturo Cobb and Chin-Tser Huang. 2009. Stabilization of Maximal-Metric Routing without Knowledge of Network Size. In 2009 International Conference on Parallel and Distributed Computing, Applications and Technologies, PDCAT 2009. IEEE Computer Society, Higashi Hiroshima, Japan, 306--311.

Digital Library

[10]

Z. Collin and S. Dolev. 1994. Self-Stabilizing Depth-First Search. Inform. Process. Lett. 49, 6 (1994), 297--301.

Digital Library

[11]

A. Cournier. 2009. A lower bound for the Max + 1 algorithm. https://home.mis.u-picardie.fr/~cournier/MaxPlusUn.pdf. Online; accessed 11 February 2009.

[12]

Alain Cournier. 2010. A New Polynomial Silent Stabilizing Spanning-Tree Construction Algorithm. In Structural Information and Communication Complexity, 16th International Colloquium, SIROCCO 2009 (Lecture Notes in Computer Science), Shay Kutten and Janez Zerovnik (Eds.), Vol. 5869. Springer, Piran, Slovenia, 141--153.

Digital Library

[13]

A. Cournier, S. Devismes, F. Petit, and V. Villain. 2006. Snap-stabilizing depth-first search on arbitrary networks. Comput. J. 49, 3 (2006), 268--280.

Digital Library

[14]

Alain Cournier, Stéphane Devismes, and Vincent Villain. 2005. A Snap-Stabilizing DFS with a Lower Space Requirement. In Self-Stabilizing Systems, 7th International Symposium, SSS 2005 (Lecture Notes in Computer Science), Ted Herman and Sébastien Tixeuil (Eds.), Vol. 3764. Springer, Barcelona, Spain, 33--47.

Digital Library

[15]

A. Cournier, S. Devismes, and V. Villain. 2009. Light enabling snap-stabilization of fundamental protocols. ACM Transactions on Autonomous and Adaptive Systems 4, 1 (2009), 6:1--6:27.

Digital Library

[16]

Alain Cournier, Stephane Rovedakis, and Vincent Villain. 2011. The First Fully Polynomial Stabilizing Algorithm for BFS Tree Construction. In Principles of Distributed Systems - 15th International Conference, OPODIS 2011 (Lecture Notes in Computer Science), Antonio Fernández Anta, Giuseppe Lipari, and Matthieu Roy (Eds.), Vol. 7109. Springer, Toulouse, France, 159--174.

Digital Library

[17]

A. K. Datta, S. Devismes, K. Heurtefeux, L. L. Larmore, and Y. Rivierre. 2016. Competitive self-stabilizing k-clustering. Theoretical Computer Science 626 (2016), 110--133.

Digital Library

[18]

A. K. Datta, S. Gurumurthy, F. Petit, and V. Villain. 2001. Self-Stabilizing Network Orientation Algorithms In Arbitrary Rooted Networks. Stud. Inform. Univ. 1, 1 (2001), 1--22.

[19]

A. K. Datta, L. L. Larmore, and P. Vemula. 2011. An O(n)-time Self-stabilizing Leader Election Algorithm. J. Parallel and Distrib. Comput. 71, 11 (2011), 1532--1544.

Digital Library

[20]

A. K. Datta, L. L. Larmore, and P. Vemula. 2011. Self-stabilizing leader election in optimal space under an arbitrary scheduler. Theoretical Computer Science 412, 40 (2011), 5541--5561.

Digital Library

[21]

S. Devismes, D. Ilcinkas, and C. Johnen. 2016. Self-Stabilizing Disconnected Components Detection and Rooted Shortest-Path Tree Maintenance in Polynomial Steps. In 20th International Conference on Principles of Distributed Systems, (OPODIS 2016) (LIPIcs), Vol. 70. Schloss Dagstuhl, Madrid, Spain, 10:1--10:16.

[22]

S. Devismes, D. Ilcinkas, and C. Johnen. 2018. Silent Self-Stabilizing Scheme for Spanning-Tree-like Constructions. Technical Report. HAL. https://hal.archives-ouvertes.fr/hal-01667863

[23]

S. Devismes and C. Johnen. 2016. Silent self-stabilizing BFS tree algorithms revisited. J. Parallel and Distrib. Comput. 97 (2016), 11--23.

Digital Library

[24]

Edsger W. Dijkstra. 1974. Self-stabilizing Systems in Spite of Distributed Control. Commun. ACM 17, 11 (1974), 643--644.

Digital Library

[25]

Shlomi Dolev. 2000. Self-stabilization. MIT Press, Cambridge, MA, USA.

Digital Library

[26]

S. Dolev, S. Dubois, M. Potop-Butucaru, and S. Tixeuil. 2011. Stabilizing data-link over non-FIFO channels with optimal fault-resilience. Inform. Process. Lett. 111, 18 (2011), 912--920.

Digital Library

[27]

S. Dolev, M. G. Gouda, and M. Schneider. 1999. Memory Requirements for Silent Stabilization. Acta Informatica 36, 6 (1999), 447--462.

[28]

S Dolev, A Israeli, and S Moran. 1993. Self-stabilization of dynamic systems assuming only Read/Write atomicity. Distributed Computing 7, 1 (1993), 3--16.

Digital Library

[29]

Felix C. Gärtner. 2003. A Survey of Self-Stabilizing Spanning-Tree Construction Algorithms. Technical Report. Swiss Federal Institute of Technolog (EPFL).

[30]

Christian Glacet, Nicolas Hanusse, David Ilcinkas, and Colette Johnen. 2014. Disconnected Components Detection and Rooted Shortest-Path Tree Maintenance in Networks. In Stabilization, Safety, and Security of Distributed Systems - 16th International Symposium, SSS 2014 (Lecture Notes in Computer Science), Pascal Felber and Vijay K. Garg (Eds.), Vol. 8756. Springer, Paderborn, Germany, 120--134.

[31]

C. Glacet, N. Hanusse, D. Ilcinkas, and C. Johnen. 2016. Disconnected Components Detection and Rooted Shortest-Path Tree Maintenance in Networks - extended version. Technical Report. LaBRI, CNRS UMR 5800. https://hal.archives-ouvertes.fr/hal-01352245

[32]

M. G. Gouda and T. Herman. 1991. Adaptive Programming. IEEE Trans. Software Eng. 17, 9 (1991), 911--921.

Digital Library

[33]

Shing-Tsaan Huang and Nian-Shing Chen. 1992. A Self-Stabilizing Algorithm for Constructing Breadth-First Trees. Inform. Process. Lett. 41, 2 (1992), 109--117.

Digital Library

[34]

A. Kosowski and L. Kuszner. 2005. A Self-stabilizing Algorithm for Finding a Spanning Tree in a Polynomial Number of Moves. In 6th International Conference Parallel Processing and Applied Mathematics, (PPAM'05) (Lecture Notes in Computer Science), Vol. 3911. Springer, Poznan, Poland, 75--82.

Digital Library

[35]

Alberto Leon-Garcia and Indra Widjaja. 2004. Communication Networks (2 ed.). McGraw-Hill, Inc., New York, NY, USA.

Digital Library

[36]

Morris Sloman and Jeff Kramer. 1987. Distributed systems and computer networks. Prentice Hall International (UK) Ltd., Hertfordshire, UK, UK.

Digital Library

[37]

G Tel. Second edition 2001. Introduction to distributed algorithms. Cambridge University Press, Cambridge, UK.

Digital Library

Cited By

Devismes SIlcinkas DJohnen C(2022)Optimized Silent Self-Stabilizing Scheme for Tree-Based ConstructionsAlgorithmica10.1007/s00453-021-00878-984:1(85-123)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1007/s00453-021-00878-9
Altisen KDevismes SDurand A(2018)Acyclic Strategy for Silent Self-stabilization in Spanning ForestsStabilization, Safety, and Security of Distributed Systems10.1007/978-3-030-03232-6_13(186-202)Online publication date: 20-Oct-2018
https://doi.org/10.1007/978-3-030-03232-6_13

Index Terms

Silent self-stabilizing scheme for spanning-tree-like constructions
1. Theory of computation
  1. Models of computation
    1. Concurrency
      1. Distributed computing models

Recommendations

Optimized Silent Self-Stabilizing Scheme for Tree-Based Constructions
Abstract
We propose a general scheme to compute tree-based data structures on arbitrary networks. This scheme is self-stabilizing, silent, and despite its generality, also efficient. It is written in the locally shared memory model with composite atomicity ... $_{}$ $_{}$
Read More
A self-stabilizing memory efficient algorithm for the minimum diameter spanning tree under an omnipotent daemon
Abstract
Routing protocols are at the core of distributed systems performances, especially in the presence of faults. A classical approach to this problem is to build a spanning tree of the distributed system. Numerous spanning tree ...
Highlights
- A self-stabilizing algorithm for the minimum diameter spanning tree construction problem is proposed.
Read More
A Self-stabilizing Minimum Average Stretch Spanning Tree Construction
Networked Systems
Abstract
Stretch is a metric in the construction of spanning trees that measures the deviation in the distance between a pair of nodes in the tree compared to its shortest distance in the underlying graph. This paper proposes a silent self-stabilizing low ... $^{}$
Read More

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

ICDCN '19: Proceedings of the 20th International Conference on Distributed Computing and Networking

January 2019

535 pages

ISBN:9781450360944

DOI:10.1145/3288599

General Chairs:
R. C. Hansdah
IISc Bangalore, India Paolo Bellavista, University of Bologna, Italy
,
Dilip Krishnaswamy
Reliance Jio Infocomm, India Sriram V. Pemmaraju, University of Iowa
,
Nitin Vaidya
Georgetown University

Copyright © 2019 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

SIGOPS: ACM Special Interest Group on Operating Systems
Indian Institute of Science: Indian Institute of Science

In-Cooperation

ACM: Association for Computing Machinery

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 04 January 2019

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

ICDCN '19

Sponsor:

SIGOPS
Indian Institute of Science

ICDCN '19: International Conference on Distributed Computing and Networking

January 4 - 7, 2019

Bangalore, India

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
46
Total Downloads

Downloads (Last 12 months)1
Downloads (Last 6 weeks)0

Other Metrics

View Author Metrics

Citations

Cited By

Devismes SIlcinkas DJohnen C(2022)Optimized Silent Self-Stabilizing Scheme for Tree-Based ConstructionsAlgorithmica10.1007/s00453-021-00878-984:1(85-123)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1007/s00453-021-00878-9
Altisen KDevismes SDurand A(2018)Acyclic Strategy for Silent Self-stabilization in Spanning ForestsStabilization, Safety, and Security of Distributed Systems10.1007/978-3-030-03232-6_13(186-202)Online publication date: 20-Oct-2018
https://doi.org/10.1007/978-3-030-03232-6_13

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

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents