Self-stabilizing depth-first token circulation in arbitrary rooted networks

  • Authors:

  • Ajoy K. Datta;Colette Johnen;Franck Petit;Vincent Villain

  • Affiliations:

  • Department of Computer Science, University of Nevada, Las Vegas, NV;L.R.I./C.N.R.S., Université de Paris-Sud, 91405 Orsay Cedex, France;LaRIA, Université de Picardie Jules Verne, rue du Moulin Neuf, 80000 Amiens, France;LaRIA, Université de Picardie Jules Verne, rue du Moulin Neuf, 80000 Amiens, France

  • Venue:
  • Distributed Computing
  • Year:
  • 2000

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Abstract

We present a deterministic distributed depth-first token passing protocol on a rooted network. This protocol uses neither the processor identifiers nor the size of the network, but assumes the existence of a distinguished processor, called the root of the network. The protocol is self-stabilizing, meaning that starting from an arbitrary state (in response to an arbitrary perturbation modifying the memory state), it is guaranteed to reach a state with no more than one token in the network. Our protocol implements a strictly fair token circulation scheme. The proposed protocol has extremely small state requirement - only 3(Δ + 1) states per processor, i.e., O(log Δ) bits per processor, where Δ is the degree of the network. The protocol can be used to implement a strictly fair distributed mutual exclusion in any rooted network. This protocol can also be used to construct a DFS spanning tree.