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doi:10.1006/jpdc.2001.1811    
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Copyright © 2002 Elsevier Science (USA). All rights reserved.

Regular Article

Self-Stabilizing Deterministic Network Decomposition*1

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Fatima Belkoucha, Marc Buib, Liming Chenc and Ajoy K. Dattad, 2, 3

a Heudiasyc, Université de Technologie de Compiègne, France

b Laboratoire de Recherche LRIA, Université Paris 8, France

c ICTT, Département Maths/Info. Ecole Centrale de Lyon, France

d Department of Computer Science, University of Nevada, Las Vegas, Nevada


Received 14 January 2001; 
revised 25 September 2001; 
accepted 3 October 2001. ;
Available online 2 May 2002.

Abstract

We present a simple and efficient self-stabilizing protocol for the network partitioning problem. Given a graph with k2 nodes, our decomposition scheme partitions the network into connected and disjoint partitions, with k nodes per partition. The proposed algorithm starts with a spanning tree of the graph, but uses some links which do not belong to the tree, if necessary. The protocol is self-stabilizing meaning that starting from an arbitrary state, it is guaranteed to reach a state where the network is correctly partitioned. The protocol stabilizes in 3(h+1) rounds, where h is the height of the tree. We also propose solutions to the case where the network size is nk2. Hence our protocol works for dynamic systems in the sense that the protocol can adapt to changes of the network size. We discuss an important application of the proposed protocol.

Author Keywords: network decomposition; quorum systems; self-stabilization; spanning tree

*1 An earlier version of this paper was presented at the International Conference on High Performance Computing, Calcutta, India, December 17-20, 1999.

2 Contact author: Ajoy K. Datta. E-mail: datta@cs.unlv.edu. Fax: 702 895-4075.

3 Supported in part by a sabbatical leave grant from University of Nevada, Las Vegas.


 
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