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Time Optimal Synchronous Self Stabilizing Spanning Tree

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Distributed Computing (DISC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8205))

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Abstract

In this research, we present the first time-optimal self stabilizing algorithm for synchronous distributed spanning tree construction, assuming the standard shared registers size (O(logn) bits, where n stands for the number of processes in the system), or, similarly, standard message size. Previous algorithms with O(diameter) stabilization time complexity assumed that a larger message can be sent through each link in one time unit. Hence, when assuming the standard message size, the time complexity of previous algorithms was not O(diameter). The current algorithm stabilizes in O(diameter) time without having previous knowledge of the network size or diameter. The only assumption we make is that we have some polynomial (possibly very large) given upper bound on the network size. However, the time complexity of the algorithm does not depend on that upper bound. Using our results, most known distributed global tasks, such as distributed reset, can be performed in a relatively easy way and in optimal time. As a building block, we present a new self stabilizing silent phase clock algorithm for synchronous networks (based on a known non-silent algorithm). It is optimal in time too. We believe it may be an interesting contribution by itself.

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References

  1. Afek, Y., Bremler-Barr, A.: Self-stabilizing unidirectional network algorithms by power supply. Chicago J. Theor. Comput. Sci. (1998)

    Google Scholar 

  2. Afek, Y., Kutten, S., Yung, M.: Memory-efficient self stabilizing protocols for general networks. In: van Leeuwen, J., Santoro, N. (eds.) WDAG 1990. LNCS, vol. 486, pp. 15–28. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  3. Afek, Y., Kutten, S., Yung, M.: The local detection paradigm and its application to self-stabilization. Theor. Comput. Sci., 199–229 (1997)

    Google Scholar 

  4. Aggarwal, S., Kutten, S.: Time optimal self-stabilizing spanning tree algorithms. In: Shyamasundar, R.K. (ed.) FSTTCS 1993. LNCS, vol. 761, pp. 400–410. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  5. Arora, A., Gouda, M.G.: Distributed reset. In: Veni Madhavan, C.E., Nori, K.V. (eds.) FSTTCS 1990. LNCS, vol. 472, pp. 316–331. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Awerbuch, B., Cidon, I., Kutten, S.: Optimal maintenance of a spanning tree. J. ACM 55(4) (2008)

    Google Scholar 

  8. Awerbuch, B., Kutten, S., Mansour, Y., Patt-Shamir, B., Varghese, G.: A time-optimal self-stabilizing synchronizer using a phase clock. IEEE Trans. Dependable Sec. Comput. 4(3), 180–190 (2007)

    Article  Google Scholar 

  9. Awerbuch, B., Mansour, Y., Kutten, S., Patt-Shamir, B., Varghese, G.: Time optimal self-stabilizing synchronization. In: STOC, pp. 652–661 (1993)

    Google Scholar 

  10. Awerbuch, B., Patt-Shamir, B., Varghese, G.: Self-stabilization by local checking and correction. In: FOCS, pp. 268–277 (1991)

    Google Scholar 

  11. Boulinier, C., Petit, F., Villain, V.: When graph theory helps self-stabilization. In: PODC, pp. 150–159 (2004)

    Google Scholar 

  12. Burman, J., Kutten, S.: Time optimal asynchronous self-stabilizing spanning tree. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 92–107. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Petit, F., Boulinier, C., Villain, V.: Synchronous vs. asynchronous unison. Algoritmica 51(1), 61–80 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  15. Cournier, A.: A new polynomial silent stabilizing spanning-tree construction algorithm, 141–153 (2009)

    Google Scholar 

  16. Datta, A.K., Larmore, L.L., Piniganti, H.: Self-stabilizing leader election in dynamic networks. In: Dolev, S., Cobb, J., Fischer, M., Yung, M. (eds.) SSS 2010. LNCS, vol. 6366, pp. 35–49. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Datta, A.K., Larmore, L.L., Vemula, P.: An o(n)-time self-stabilizing leader election algorithm. J. Parallel Distrib. Comput. 71(11), 1532–1544 (2011)

    Article  MATH  Google Scholar 

  18. Dijkstra, E.W.: Self stabilization in spite of distributed control. Comm. ACM 17, 167–180 (1974)

    Article  MathSciNet  Google Scholar 

  19. Dolev, D., Shavit, N.: Bounded concurrent time-stamping. SIAM J. Comput., 418–455 (1997)

    Google Scholar 

  20. Dolev, S., Israeli, A., Moran, S.: Self-stabilization of dynamic systems assuming only read/write atomicity. In: PODC, pp. 103–117 (1990)

    Google Scholar 

  21. Dubois, S., Guerraoui, R.: Introducing speculation in self-stabilization: an application to mutual exclusion. In: PODC, pp. 290–298 (2013)

    Google Scholar 

  22. Gallager, R.G., Humblet, P.A., Spira, P.M.: A distributed algorithm for minimum-weight spanning trees. ACM Trans. Program. Lang. Syst. 5(1), 66–77 (1983)

    Article  MATH  Google Scholar 

  23. Gosh, S., Gupta, A., Pemmaraju, S.V.: A fault containing self stabilizing algorithm for spanning trees. Journal of Computing and Information 2, 322–338 (1996)

    Google Scholar 

  24. Gouda, M.G., Herman, T.: Stabilizing unison. Inf. Process. Lett. 35(4), 171–175 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  25. Herman, T., Ghosh, S.: Stabilizing phase-clocks. Inf. Process. Lett. 54(5), 259–265 (1995)

    Article  MATH  Google Scholar 

  26. Kurose, J.F., Ross, K.W.: Computer Networking: A Top-Down Approach, 2nd edn. Addison Wesley (2003)

    Google Scholar 

  27. Kutten, S., Porat, A.: Maintenance of a spanning tree in dynamic networks. In: Jayanti, P. (ed.) DISC 1999. LNCS, vol. 1693, pp. 342–355. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  28. Matias, Y., Afek, Y.: Simple and efficient election algorithms for anonymous networks. In: Bermond, J.-C., Raynal, M. (eds.) WDAG 1989. LNCS, vol. 392, pp. 183–194. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  29. Peleg, D.: Distributed computing: a locality-sensitive approach. Society for Industrial and Applied Mathematics (2000)

    Google Scholar 

  30. Perlman, R.J.: Fault-tolerant broadcast of routing information. Computer Networks 7, 395–405 (1983)

    Google Scholar 

  31. Dolev, S., Israeli, A., Moran, S.: Uniform dynamic self-stabilizing leader election. In: Toueg, S., Kirousis, L.M., Spirakis, P.G. (eds.) WDAG 1991. LNCS, vol. 579, pp. 167–180. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Information Systems Engineering, IE, Technion, Haifa, Israel

    Alex Kravchik & Shay Kutten

Authors
  1. Alex Kravchik
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  2. Shay Kutten
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Editor information

Editors and Affiliations

  1. Blavatnik School of Computer Sciences, Tel Aviv University, Ramat Aviv, Tel-Aviv, Israel

    Yehuda Afek

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Kravchik, A., Kutten, S. (2013). Time Optimal Synchronous Self Stabilizing Spanning Tree. In: Afek, Y. (eds) Distributed Computing. DISC 2013. Lecture Notes in Computer Science, vol 8205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41527-2_7

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  • DOI: https://doi.org/10.1007/978-3-642-41527-2_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41526-5

  • Online ISBN: 978-3-642-41527-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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