Self-stabilizing Population Protocols
Self-stabilization in a model of anonymous, asynchronous interacting agents deployed in a network of unknown size is considered. Dijkstra-style round-robin token circulation can be done deterministically with constant space per node in this model. Constant-space protocols are given for leader election in rings, local-addressing in degree-bounded graphs, and establishing consistent global direction in an undirected ring. A protocol to construct a spanning tree in regular graphs using O(logD) memory is also given, where D is the diameter of the graph. A general method for eliminating nondeterministic transitions from the self-stabilizing implementation of a large family of behaviors is used to simplify the constructions, and general conditions under which protocol composition preserves behavior are used in proving their correctness.
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