Abstract
This paper considers the self-stabilizing unison problem. The contribution of this paper is threefold. First, we establish that when any self-stabilizing asynchronous unison protocol runs in synchronous systems, it converges to synchronous unison if the size of the clock K is greater than C G , C G being the length of the maximal cycle of the shortest maximal cycle basis if the graph contains cycles, 2 otherwise (tree networks). The second result demonstrates that the asynchronous unison in [3] provides a universal self-stabilizing synchronous unison for trees which is optimal in memory space. It works with any K ≥ 3, without any extra state, and stabilizes within 2D rounds, where D is the diameter of the network. This protocol gives a positive answer to the question whether there exists or not a universal self-stabilizing synchronous unison for tree networks with a state requirement independant of local or global information of the tree. If K = 3, then the stabilization time of this protocol is equal to D only, i.e., it reaches the optimal performance of [8]. The third result of this paper is a self-stabilizing unison for general synchronous systems. It requires K ≥ 2 only, at least K+D states per process, and its stabilization time is 2D only. This is the best solution for general synchronous systems, both for the state requirement and the stabilization time.
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© 2005 Springer-Verlag Berlin Heidelberg
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Boulinier, C., Petit, F., Villain, V. (2005). Synchronous vs. Asynchronous Unison. In: Tixeuil, S., Herman, T. (eds) Self-Stabilizing Systems. SSS 2005. Lecture Notes in Computer Science, vol 3764. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11577327_2
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DOI: https://doi.org/10.1007/11577327_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29814-4
Online ISBN: 978-3-540-32123-1
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