Correctness of Self-stabilizing Algorithms under the Dolev Model When Adapted to Composite Atomicity Models

  • Chih-Yuan Chen
  • Cheng-Pin Wang
  • Tetz C. Huang
  • Ji-Cherng Lin
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 21)

Abstract

In this paper, we first clarify that it is not a trivial matter whether or not a self-stabilizing algorithm under the Dolev model, when adapted to a composite atomicity model, is also self-stabilizing. Then we employ a particular “simulation” approach to show that if a self-stabilizing algorithm under the Dolev model has one of two certain forms, then it is also self-stabilizing when adapted to one of the composite atomicity models, the fair daemon model. Since most existing self-stabilizing algorithms under the Dolev model have the above-mentioned forms, our results imply that they are all self-stabilizing when adapted to the fair daemon model.

Keywords

Silent self-stabilizing algorithm Composite atomicity Read/write atomicity Fair daemon model Adaptation of algorithm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Burns, J.E.: Self-stabilizing Rings without Daemons. Technical report, Georgia Tech (1987)Google Scholar
  2. 2.
    Collin, Z., Dolev, S.: Self-stabilizing Depth-first Search. Inform. Process. Lett. 49, 297–301 (1994)MATHCrossRefGoogle Scholar
  3. 3.
    Dijkstra, E.W.: Self-stabilizing Systems in Spite of Distributed Control. Comm. ACM 17, 643–644 (1974)MATHCrossRefGoogle Scholar
  4. 4.
    Dolev, S.: Self-stabilization. MIT Press (2000)Google Scholar
  5. 5.
    Dolev, S., Israeli, A., Moran, S.: Self-stabilization of Dynamic Systems Assuming Only Read/Write Atomicity. In: 9th Annual ACM Symposium on Principles of Distributed Computing, Quebec, Canada, pp. 103–117 (1990)Google Scholar
  6. 6.
    Dolev, S., Israeli, A., Moran, S.: Self-stabilization of Dynamic Systems Assuming Only Read/Write Atomicity. Distrib. Comput. 7, 3–16 (1993)CrossRefGoogle Scholar
  7. 7.
    Ghosh, S., Gupta, A.: An Exercise in Fault-containment: Self-stabilizing Leader Election. Inform. Process. Lett. 59, 281–288 (1996)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Ghosh, S., Gupta, A., Herman, T., Pemmaraju, S.V.: Fault-containing Self-stabilizing Algorithm. In: 15th ACM Symposium on Principles of Distributed Computing, Philadelphia, USA, pp. 45–54 (1996)Google Scholar
  9. 9.
    Ghosh, S., Gupta, A., Pemmaraju, S.V.: A Fault-containing Self-stabilizing Spanning Tree Algorithm. J. Comput. Inform. 2, 322–338 (1996)Google Scholar
  10. 10.
    Huang, T.C.: A Self-stabilizing Algorithm for the Shortest Path Problem Assuming Read/Write Atomicity. J. Comput. Syst. Sci. 71, 70–85 (2005)MATHCrossRefGoogle Scholar
  11. 11.
    Huang, S.T., Chen, N.S.: A Self-stabilizing Algorithm for Constructing Breadth-first Trees. Inform. Process. Lett. 41, 109–117 (1992)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Hsu, S.C., Huang, S.T.: A Self-stabilizing Algorithm for Maximal Matching. Inform. Process. Lett. 43, 77–81 (1992)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Huang, T.C., Lin, J.C.: A Self-stabilizing Algorithm for the Shortest Path Problem in a Distributed System. Comput. Math. Appl. 43, 103–109 (2002)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Huang, T.C., Lin, J.C., Chen, H.J.: A Self-stabilizing Algorithm which Finds a 2-center of a Tree. Comput. Math. Appl. 40, 607–624 (2000)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Huang, T.C., Lin, J.C., Chen, C.Y., Wang, C.P.: A Self-stabilizing Algorithm for Finding a Minimal 2-dominating Set Assuming the Distributed Demon Model. Comput. Math. Appl. 54, 350–356 (2007)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Huang, T.C., Lin, J.C., Mou, N.: A Self-stabilizing Algorithm for the Center-finding Problem Assuming Read/Write Atomicity. Comput. Math. Appl. 48, 1667–1676 (2004)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Ikeda, M., Kamei, S., Kakugawa, H.: A Space-optimal Self-stabilizing Algorithm for the Maximal Independent Set Problem. In: 3rd International Conference on Parallel and Distributed Computing, Applications and Technologies, Kanazawa, Japan, pp. 70–74 (2002)Google Scholar
  18. 18.
    Shukla, S., Rosenkrantz, D.J., Ravi, S.S.: Observations on Self-stabilizing Graph Algorithms on Anonymous Networks. In: 2nd Workshop on Self-stabilizing Systems, p. 7.1–7.15. Las Vegas, USA (1995)Google Scholar
  19. 19.
    Tsin, Y.H.: An Improved Self-stabilizing Algorithm for Biconnectivity and Bridge-connectivity. Inform. Process. Lett. 102, 27–34 (2007)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Turau, V.: Linear Self-stabilizing Algorithms for the Independent and Dominating Set Problems Using an Unfair Distributed Scheduler. Inform. Process. Lett. 103, 88–93 (2007)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Turau, V., Hauck, B.: A Self-stabilizing Algorithm for Constructing Weakly Connected Minimal Dominating Sets. Inform. Process. Lett. 109, 763–767 (2009)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Tzeng, C.H., Jiang, J.R., Huang, S.T.: A Self-stabilizing (Δ + 4)-edge-coloring Algorithm for Planar Graphs in Anonymous Uniform Systems. Inform. Process. Lett. 101, 168–173 (2007)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Chih-Yuan Chen
    • 1
  • Cheng-Pin Wang
    • 2
  • Tetz C. Huang
    • 3
  • Ji-Cherng Lin
    • 3
  1. 1.Department of Computer Science and Information EngineeringTaoyuan Innovation Institute of TechnologyChung-LiTaiwan
  2. 2.General Education CenterTzu Chi College of TechnologyHualienTaiwan
  3. 3.Department of Computer Science and EngineeringYuan-Ze UniversityChung-LiTaiwan

Personalised recommendations