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Journal of Information Science and Engineering, Vol. 26 No. 4, pp. 1307-1322 (July 2010)

Size-Independent Self-Stabilizing Asynchronous Phase Synchronization in General Graphs*

CHI-HUNG TZENG, JEHN-RUEY JIANG+ AND SHING-TSAAN HUANG+
Department of Electronic Engineering and Institute of Computer and Communication Engineering
National Taipei University of Technology
Taipei, 106 Taiwan
E-mail: tylee@ntut.edu.tw
+Department of Computer Science and Information Engineering
Nanhua University
Chiayi, 622 Taiwan
E-mail: chun@mail.mhu.edu.tw

In this paper, we design a self-stabilizing phase synchronizer for distributed systems. The synchronizer enables a node to transfer from one phase to the next one, subject to the condition that at most two consecutive phases appear among all nodes. It does not rely on any system parameter like the number of nodes, and thus fits for dynamic systems where nodes can freely join or leave. Each node just maintains a few variables that are related to its neighborhood; all operations are decided based on local information rather than global information. The memory usage of the proposed algorithm is low; each node has only O(GK) states, where G is the maximum degree of nodes and K > 1 is the number of phases. To the best of our knowledge, there are no other such size-independent self-stabilizing algorithms for systems of general graph topologies.

Keywords: general connected graph, fault tolerance, phase synchronization, self-stabilization, spanning tree

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Received June 2, 2008; revised April 1, 2009; accepted June 30, 2009.
Communicated by Sy-Yen Kuo.
* This was an extended version of the paper entitled Self-Stabilizing Asynchronous Phase Synchronization in General Graphs, presented in the 8th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2006), November, 17th-19th, 2006, Dallas, Texas, U.S.A.