Self-stabilizing deterministic network decomposition

  • Authors:
  • Fatima Belkouch;Marc Bui;Liming Chen;Ajoy K. Datta

  • Affiliations:
  • Heudiasyc, Université de Technologie de Compiègne, France;Laboratoire de Recherche LRIA, Université Paris 8, France;ICTT, Départment Maths/Info., Ecole Centrale de Lyon, France;Department of Computer Science, University of Nevada, Las Vegas, Nevada

  • Venue:
  • Journal of Parallel and Distributed Computing
  • Year:
  • 2002

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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 n ≤ k2. 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.