Distributed self-stabilizing algorithm for minimum spanning tree construction

  • Gheorghe Antonoiul
  • Pradip K. Srimani
Workshop 04+08+13: Parallel and Distributed Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1300)


Minimal Spanning Tree (MST) problem in an arbitrary undirected graph is an important problem in graph theory and has extensive applications. Numerous algorithms are available to compute an MST. Our purpose here is to propose a self-stabilizing distributed algorithm for the MST problem and to prove its correctness. The algorithm utilizes an interesting result of [MP88]. We show the correctness of the proposed algorithm by using a new technique involving induction.


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  1. [ADG92]
    A. Arora, S. Dolev, and M. Gouda. Maintaining digital clocks in step. Parallel Processing Letters, 1(1):11–18, 1992.Google Scholar
  2. [Agg94]
    S. Aggrawal. Time optimal self-stabilizing spanning tree algorithms. Technical Report MIT/LCS/TR-632, Massachusetts Institute of Technology, May 1994.Google Scholar
  3. [AS95]
    G. Antonoiu and P. K. Srimani. A self-stabilizing distributed algorithm to construct an arbitrary spanning tree of a connected graph. Computers Mathematics and Applications, 30(9):1–7, September 1995.Google Scholar
  4. [BGW89]
    G. M. Brown, M. G. Gouda, and C. L. Wu. Token systems that self-stabilize. IEEE Trans. Comput., 38(6):845–852, June 1989.Google Scholar
  5. [CYH91]
    N. S. Chen, H. P. Yu, and S. T. Huang. A self-stabilizing algorithm for constructing spanning trees. Inf. Processing Letters, 39(3):14–151, 1991.Google Scholar
  6. [Dij74]
    E. W. Dijkstra. Self-stabilizing systems in spite of distributed control. Communications of the ACM, 17(11):634–644, November 1974.Google Scholar
  7. [FD92]
    M. Flatebo and A. K. Datta. Two-State self-Stabilizing algorithms. In Proceedings of the IPPS-92, California, June 1992.Google Scholar
  8. [HC92]
    S.T. Huang and N.-S. Chen. A self-stabilizing algorithm for constructing breadth first trees. Inf. Processing Letters, 41:109–117, January 1992.Google Scholar
  9. [HS84]
    E. Horowitz and S. Sahni. Fundamentals of Computer Algorithms. Computer Science Press, 1984.Google Scholar
  10. [Lam84]
    L. Lamport. Solved problems, unsolved problems, and non-problems in concurrency. In Proceedings of the 3rd Annual ACM Symposium on Principles of Distributed Computing, pages 1–11, 1984.Google Scholar
  11. [MP88]
    B. M. Maggs and S. A. Plotkin. Minimum-cost spanning tree as a path finding problem. Information Processing Letters, 26:291–293, January 1988.Google Scholar
  12. [Sch93]
    M. Schneider. Self-stabilization. ACM Computing Surveys, 25(1):45–67, March 1993.Google Scholar
  13. [SS92]
    S. Sur and P. K. Srimani. A self-stabilizing distributed algorithm to construct BFS spanning tress of a symmetric graph. Parallel Processing Letters, 2(2,3):171–180, September 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Gheorghe Antonoiul
    • 1
  • Pradip K. Srimani
    • 1
  1. 1.Department of Computer ScienceColorado State UniversityFt. Collins

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