Skip to main content
SpringerLink
Log in

A Self-stabilizing Minimum Average Stretch Spanning Tree Construction

  • Conference paper
  • First Online:
Networked Systems (NETYS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13464))

Included in the following conference series:

  • 285 Accesses

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 stretch spanning tree construction protocol BuildTree , that is based on a Low Diameter Decomposition (LDD) technique. The LDD involves steps wherein the graph is decomposed into a small number of connected blocks or clusters, each having a low diameter value. The proposed BuildTree algorithm generates a spanning tree with an average stretch of \(n^{\mathcal {O}(1)}\) and converges to a correct configuration in \(\mathcal {O}(n+\varDelta \cdot \eta )\) rounds, where n, \(\varDelta \) and \(\eta \) is the number of nodes in the graph, the maximum size of a cluster and the number of clusters, respectively. To the best of our knowledge, this is the first known work of using self-stabilization in order to make low stretch tree constructions fault-tolerant.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    It is clear that BuildTree protocol takes \(\mathcal {O}(n\cdot \log n)\) bits of space at each node for its execution.

References

  1. Abraham, I., Neiman, O.: Using petal-decompositions to build a low stretch spanning tree. In: Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing, pp. 395–406 (2012)

    Google Scholar 

  2. Alon, N., Karp, R.M., Peleg, D., West, D.: A graph-theoretic game and its application to the k-server problem. SIAM J. Comput. 24(1), 78–100 (1995)

    Article  MathSciNet  Google Scholar 

  3. Arora, A., Gouda, M., Herman, T.: Composite routing protocols. In: Proceedings of the Second IEEE Symposium on Parallel and Distributed Processing 1990, pp. 70–78. IEEE (1990)

    Google Scholar 

  4. Awerbuch, B.: Complexity of network synchronization. J. ACM (JACM) 32(4), 804–823 (1985)

    Article  MathSciNet  Google Scholar 

  5. Bartal, Y.: Probabilistic approximation of metric spaces and its algorithmic applications. In: Proceedings of 37th Conference on Foundations of Computer Science, pp. 184–193. IEEE (1996)

    Google Scholar 

  6. Becker, R., Emek, Y., Ghaffari, M., Lenzen, C.: Distributed algorithms for low stretch spanning trees. In: 33rd International Symposium on Distributed Computing (DISC 2019), vol. 146, p. 4 (2019)

    Google Scholar 

  7. Borradaile, G., Chambers, E.W., Eppstein, D., Maxwell, W., Nayyeri, A.: Low-stretch spanning trees of graphs with bounded width. arXiv preprint arXiv:2004.08375 (2020)

  8. Bui, A., Datta, A.K., Petit, F., Villain, V.: Snap-stabilization and PIF in tree networks. Distrib. Comput. 20(1), 3–19 (2007)

    MATH  Google Scholar 

  9. Caron, E., Datta, A.K., Depardon, B., Larmore, L.L.: A self-stabilizing K-clustering algorithm using an arbitrary metric. In: Sips, H., Epema, D., Lin, H.-X. (eds.) Euro-Par 2009. LNCS, vol. 5704, pp. 602–614. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03869-3_57

    Chapter  Google Scholar 

  10. Chen, N.S., Yu, H.P., Huang, S.T.: A self-stabilizing algorithm for constructing spanning trees. Inf. Process. Lett. 39(3), 147–151 (1991)

    Article  MathSciNet  Google Scholar 

  11. Cournier, A.: A new polynomial silent stabilizing spanning-tree construction algorithm. In: Kutten, S., Žerovnik, J. (eds.) SIROCCO 2009. LNCS, vol. 5869, pp. 141–153. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11476-2_12

    Chapter  Google Scholar 

  12. Deo, N., Prabhu, G., Krishnamoorthy, M.S.: Algorithms for generating fundamental cycles in a graph. ACM Trans. Math. Softw. (TOMS) 8(1), 26–42 (1982)

    Article  MathSciNet  Google Scholar 

  13. Devismes, S., Ilcinkas, D., Johnen, C.: Self-stabilizing disconnected components detection and rooted shortest-path tree maintenance in polynomial steps. arXiv preprint arXiv:1703.03315 (2017)

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

    Article  Google Scholar 

  15. Dijkstra, E.W.: Self-stabilization in spite of distributed control. In: Dijkstra, E.W. (ed.) Selected Writings on Computing: A Personal Perspective, pp. 41–46. Springer, New York (1982). https://doi.org/10.1007/978-1-4612-5695-3_7

    Chapter  MATH  Google Scholar 

  16. Ding, Y.: Fault tolerance in distributed systems using self-stabilization (2014)

    Google Scholar 

  17. Dolev, S.: Self-stabilization, March 2000 (2000)

    Google Scholar 

  18. Dolev, S., Gouda, M.G., Schneider, M.: Memory requirements for silent stabilization. Acta Informatica 36(6), 447–462 (1999)

    Article  MathSciNet  Google Scholar 

  19. Ghaffari, M., Karrenbauer, A., Kuhn, F., Lenzen, C., Patt-Shamir, B.: Near-optimal distributed maximum flow. In: Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, pp. 81–90 (2015)

    Google Scholar 

  20. Ghosh, S.: Distributed Systems: An Algorithmic Approach. Chapman and Hall/CRC, Boca Raton (2014)

    Book  Google Scholar 

  21. Gurjar, A., Peri, S., Sengupta, S.: Distributed and fault-tolerant construction of low stretch spanning tree. In: 2020 19th International Symposium on Parallel and Distributed Computing (ISPDC), pp. 142–149. IEEE (2020)

    Google Scholar 

  22. Harvey, N.: Low-stretch trees. https://www.cs.ubc.ca/~nickhar/Cargese1.pdf. Accessed 19 Feb 2022

  23. Huang, S.T., Chen, N.S.: A self-stabilizing algorithm for constructing breadth-first trees. Inf. Process. Lett. 41(2), 109–117 (1992)

    Article  MathSciNet  Google Scholar 

  24. Johnen, C., Tixeuil, S.: Route preserving stabilization. In: Huang, S.-T., Herman, T. (eds.) SSS 2003. LNCS, vol. 2704, pp. 184–198. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-45032-7_14

    Chapter  Google Scholar 

  25. Kosowski, A., Kuszner, Ł.: A self-stabilizing algorithm for finding a spanning tree in a polynomial number of moves. In: Wyrzykowski, R., Dongarra, J., Meyer, N., Waśniewski, J. (eds.) PPAM 2005. LNCS, vol. 3911, pp. 75–82. Springer, Heidelberg (2006). https://doi.org/10.1007/11752578_10

  26. Larsson, A., Tsigas, P.: Self-stabilizing (k,r)-clustering in wireless ad-hoc networks with multiple paths. In: Lu, C., Masuzawa, T., Mosbah, M. (eds.) OPODIS 2010. LNCS, vol. 6490, pp. 79–82. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17653-1_6

    Chapter  Google Scholar 

  27. Nguyen, M.H., Hà, M.H., Nguyen, D.N., et al.: Solving the k-dominating set problem on very large-scale networks. Comput. Soc. Netw. 7(1), 1–15 (2020)

    Article  Google Scholar 

  28. Peleg, D., Roditty, L., Tal, E.: Distributed algorithms for network diameter and girth. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012. LNCS, vol. 7392, pp. 660–672. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31585-5_58

    Chapter  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Hyderabad, India

    Sinchan Sengupta, Sathya Peri & Parwat Singh Anjana

Authors
  1. Sinchan Sengupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sathya Peri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Parwat Singh Anjana
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sinchan Sengupta .

Editor information

Editors and Affiliations

  1. Mohammed First University, Oujda, Morocco

    Mohammed-Amine Koulali

  2. Technical University of Darmstadt, Darmstadt, Germany

    Mira Mezini

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sengupta, S., Peri, S., Anjana, P.S. (2022). A Self-stabilizing Minimum Average Stretch Spanning Tree Construction. In: Koulali, MA., Mezini, M. (eds) Networked Systems. NETYS 2022. Lecture Notes in Computer Science, vol 13464. Springer, Cham. https://doi.org/10.1007/978-3-031-17436-0_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-17436-0_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-17435-3

  • Online ISBN: 978-3-031-17436-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation