Self-stabilizing symmetry breaking in constant-space (extended abstract)

We investigate the problem of self-stabilizing round-robin token management scheme on an anonymous bidirectional ring of identical processors, where each processor is an asynchronous probabilistic (coin-flipping) finite state machine which sends and receives messages. We show that the solution to this problem is equivalent to symmetry breaking (i.e., leader election). Requiring only constant-size messages and message-passing model has practical implications: our solution can be implemented in high-speed networks using a universal fast hardware switches (i.e., finite state machines) of size independent of the size of the network.

[1]  Alon Itai On the computational power needed to elect a leader , 1990 .

[2]  Nancy A. Lynch,et al.  Electing a leader in a synchronous ring , 1987, JACM.

[3]  Alon Itai,et al.  Symmetry breaking in distributive networks , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[4]  Nancy A. Lynch,et al.  Distributed Computing: Models and Methods , 1990, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[5]  Baruch Schieber,et al.  Calling names in nameless networks , 1989, PODC '89.

[6]  Yishay Mansour,et al.  On the bit complexity of distributed computations in a ring with a leader , 1986, PODC '86.

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

[8]  Mohamed G. Gouda,et al.  Token Systems that Self-Stabilize , 1989, IEEE Trans. Computers.

[9]  Amos Israeli,et al.  Self-Stabilizing Ring Orientation , 1990, WDAG.

[10]  Amos Israeli,et al.  Resource bounds for self stabilizing message driven protocols , 1991, PODC '91.

[11]  H. Ohnishi,et al.  ATM ring protocol and performance , 1989, IEEE International Conference on Communications, World Prosperity Through Communications,.

[12]  Amos Israeli,et al.  Token management schemes and random walks yield self-stabilizing mutual exclusion , 1990, PODC '90.

[13]  Noga Alon,et al.  Coin-flipping games immune against linear-sized coalitions , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[14]  Nicola Santoro,et al.  Breaking Symmetry in Synchronous Networks , 1986, Aegean Workshop on Computing.

[15]  Andy Hopper,et al.  The Cambridge Fast Ring Networking System , 1988, IEEE Trans. Computers.

[16]  Doron Rotem,et al.  A technique for proving lower bounds for distributed maximum-finding algorithms (Preliminary Version) , 1982, STOC '82.

[17]  Moti Yung,et al.  Memory-Efficient Self Stabilizing Protocols for General Networks , 1990, WDAG.

[18]  David G. Kirkpatrick,et al.  Probabilistic solitude verification on a ring , 1986, PODC '86.

[19]  Paul M. B. Vitányi Distributed elections in an archimedean ring of processors , 1984, STOC '84.

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

[21]  Aurel A. Lazar,et al.  MAGNET II: A Metropolitan Area Network Based on Asynchronous Time Sharing , 1990, IEEE J. Sel. Areas Commun..

[22]  Yoram Ofek,et al.  MetaRing-a full-duplex ring with fairness and spatial reuse , 1993, IEEE Trans. Commun..

[23]  F. Ross,et al.  FDDI - A tutorial , 1986, IEEE Communications Magazine.

[24]  Aurel A. Lazar,et al.  A metropolitan area network based on asynchronous time sharing , 1989, IEEE International Conference on Communications, World Prosperity Through Communications,.

[25]  Paul G. Spirakis,et al.  Symmetry Breaking in Asynchronous Rings with O(n) Messages , 1989, WDAG.

[26]  B. Awerbuch,et al.  Distributed program checking: a paradigm for building self-stabilizing distributed protocols , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[27]  Moti Yung,et al.  Principle for high speed network control: congestion-and deadlock-freeness, self-routing, and a single buffer per link , 1990, PODC '90.

[28]  Jan K. Pachl,et al.  Uniform self-stabilizing rings , 1988, TOPL.

[29]  Shmuel Katz,et al.  Self-stabilizing extensions for message-passing systems , 1990, PODC '90.

[30]  Nancy A. Lynch,et al.  The impact of synchronous communication on the problem of electing a leader in a ring , 1984, STOC '84.

[31]  Dana Angluin,et al.  Local and global properties in networks of processors (Extended Abstract) , 1980, STOC '80.

[32]  Daniel Lehmann,et al.  On the advantages of free choice: a symmetric and fully distributed solution to the dining philosophers problem , 1981, POPL '81.

[33]  Richard Cole,et al.  Deterministic coin tossing and accelerating cascades: micro and macro techniques for designing parallel algorithms , 1986, STOC '86.

[34]  Boaz Patt-Shamir,et al.  Self-stabilization by local checking and correction , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[35]  Jayadev Misra,et al.  Detecting termination of distributed computations using markers , 1983, PODC '83.