Abstract
In this paper we present lower bounds on the stabilization time for a number of graph theoretic problems, as leader election, spanning tree construction, computing the diameter, the number of nodes, the connectivity or orientation on tori, rings, hypercubes and CCC. These bounds are of the form Ω(D), where D is the diameter of the network. Moreover, time-optimal self-stabilizing algorithms for computing the orientation on tori, rings, hypercubes and CCC are presented. This gives an answer to the problem 15.4 for tori stated in [Tel94b].
This research has been partially supported by VEGA project 1/4315/97.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aggarwal, S., Kutten, S.: Time Optimal Self-Stabilizing Spanning Tree Algorithms. In Proc. of the Conference on Foundations of Software Technology and Theoretical Computer Science, LNCS 652 1993, pp. 400–410.
Awerbuch, B., Varghese, G.: Distributed Program Checking: a Paradigm for Building Self-stabilizing Distributed Protocols. In 32nd FOCS, October 1991, pp. 258–267.
Dijkstra, E. W.: Self stabilization in spite of distributed control. In Comm. ACM 17, 1974 pp. 643–644.
Dobrev, S., Ružička, P.: Linear broadcasting and N log log N election in unoriented hypercubes. In SIROCCO, 1997, to appear.
Flocchini, P., Mans, B., Santoro, N.: Sense of Direction: Formal Definitions and Properties. In SIROCCO, 1994, pp. 9–34.
Královič, R.: Time Optimal Self-Stabilizing Algorithms. Technical Report, Dept. of Computer Science, Comenius University, Bratislava, 1997. Submitted for publication.
Leighton, F. T.: Introduction to parallel algorithms and architectures: arrays, trees, hypercubes. Morgan Kaufmann Publishers, Inc., San Mateo, USA, 1992.
Prasetya, I.S.W.B., Swierstra, S.D.: Formal Design of Self-stabilizing Programs. Technical report UU-CS-1995-07, Dept. of Computer Science, Utrecht University, 1995.
Tel, G.: Network Orientation. International Journal of Foundations of Computer Science 5, 1994, pp. 23–57.
Tel, G.: Introduction to Distributed Algorithms. Cambridge University Press, Cambridge, UK, 1994.
Tel, G.: Linear election in oriented hypercubes. Parallel Processing Letters 5, 1995, pp. 357–366.
Tel, G.: Sense of Direction in Processor Networks. In SOFSEM, LNCS 1012, 1995, pp. 50–82.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Královič, R. (1997). Time optimal self-stabilizing algorithms. In: Plášil, F., Jeffery, K.G. (eds) SOFSEM'97: Theory and Practice of Informatics. SOFSEM 1997. Lecture Notes in Computer Science, vol 1338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63774-5_127
Download citation
DOI: https://doi.org/10.1007/3-540-63774-5_127
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63774-5
Online ISBN: 978-3-540-69645-2
eBook Packages: Springer Book Archive