Self-stabilizing population protocols

This article studies self-stabilization in networks of anonymous, asynchronously interacting nodes where the size of the network is unknown. Constant-space protocols are given for Dijkstra-style round-robin token circulation, leader election in rings, two-hop coloring in degree-bounded graphs, and establishing consistent global orientation in an undirected ring. A protocol to construct a spanning tree in regular graphs using O(log D) 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.

[1]  David Eisenstat,et al.  The computational power of population protocols , 2006, Distributed Computing.

[2]  Michael J. Fischer,et al.  Computation in networks of passively mobile finite-state sensors , 2004, PODC '04.

[3]  Amos Israeli,et al.  Uniform Dynamic Self-Stabilizing Leader Election , 1997, IEEE Trans. Parallel Distributed Syst..

[4]  Rafail Ostrovsky,et al.  Self-stabilizing symmetry breaking in constant-space (extended abstract) , 1992, STOC '92.

[5]  Lisa Higham,et al.  SelfStabilizing Token Circulation on Anonymous Message Passing , 1998, OPODIS.

[6]  Maria Gradinariu Potop-Butucaru,et al.  Memory space requirements for self-stabilizing leader election protocols , 1999, PODC '99.

[7]  Lisa Higham,et al.  Self-Stabilizing Token Circulation on Anonymous Message Passing Rings (Extended Abstract) , 1998 .

[8]  Hagit Attiya,et al.  Achievable cases in an asynchronous environment , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[9]  Ted Herman,et al.  Probabilistic Self-Stabilization , 1990, Information Processing Letters.

[10]  Jerrold R. Griggs,et al.  Labelling Graphs with a Condition at Distance 2 , 1992, SIAM J. Discret. Math..

[11]  Michael J. Fischer,et al.  Stably Computable Properties of Network Graphs , 2005, DCOSS.

[12]  Colette Johnen,et al.  Bounded service time and memory space optimal self-stabilizing token circulation protocol on unidirectional rings , 2004, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings..

[13]  Maria Gradinariu Potop-Butucaru,et al.  Self-stabilizing Neighborhood Unique Naming under Unfair Scheduler , 2001, Euro-Par.

[14]  Sébastien Tixeuil,et al.  A Distributed TDMA Slot Assignment Algorithm for Wireless Sensor Networks , 2004, ALGOSENSORS.

[15]  Leonid A. Levin,et al.  Fast and lean self-stabilizing asynchronous protocols , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[16]  Edsger W. Dijkstra,et al.  Self-stabilizing systems in spite of distributed control , 1974, CACM.

[17]  Mohamed G. Gouda,et al.  The Stabilizing Token Ring in Three Bits , 1996, J. Parallel Distributed Comput..

[18]  Roger Wattenhofer,et al.  Coloring unstructured radio networks , 2005, SPAA '05.

[19]  Rafail Ostrovsky,et al.  Self-Stabilizing Symmetry Breaking in Constant Space , 2002, SIAM J. Comput..

[20]  G. Chang,et al.  Labeling graphs with a condition at distance two , 2005 .

[21]  Janos Simon,et al.  Deterministic, Constant Space, Self-Stabilizing Leader Election on Uniform Rings , 1995, WDAG.