Time optimal self-stabilizing synchronization

In the network synchronization model, each node maintains a local pulse counter such that the advance of the pulse numbers simulates the advance of a clock in a synchronous network. In this paper we present a tame optimai sel&stabilizing scheme for network synchronization. Our construction has two parts. First, we give a simple rule by which each node can compute its pulse number as a function of its neighbors’ pulse numbers. This rule stabilizes in time bounded by t?te diameter of the network, it does not revoke global operations, and does not require any additional memory space. However, this rule works correctly only if the pulse numbers may grow unfoundedly. The second part of the construction (whzch is of independent interest in its own right) takes care of this problem. Specifically, we present the jirst self-stabilizing reset procedure that stabilizes in tzme proportional to the diameter of the network. This procedure can be combined with unbounded-register protocols to yield bounded-register algorithms. “Lab. for Computer Science, MIT. Supported by Air Force Contract TNDGAFOSR-86-0078, ARO contract DAAL03-86K-01 71, NSF contract CCR861 1442, DARPA contract NOOO1489-J-1988, and a special grant from IBM. t IBM T.J. Watson Research Center. $Tel-Aviv University and IBM T.J. Watson Research Center. $Lab. for Computer Science, MIT. Research partly done while visiting IBM T.J. Watson Research Center. Supported in part by DARPA contracts NOOO1 4-92J-4o33 and NOOO1492-J-1799, ONR contract NOOO14-91-J-1O46, and NSF contract 8915206-CCR. !IDEG, 55o King Street, Llttleton, MA 01460. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice ia given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. 25th ACM STOC ‘93-51931CA,USA @ J993 AG~ Q-89~9J-59 J-7/93 /QQQ51Q652,.. $J.~Q

[1]  Amos Israeli,et al.  Uniform self-stabilizing leader election , 1993 .

[2]  Eric C. Rosen,et al.  The New Routing Algorithm for the ARPANET , 1980, IEEE Trans. Commun..

[3]  Amos Israeli,et al.  Uniform Dynamic Self-Stabilizing Leader Election (Extended Absrtact) , 1991, WDAG.

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

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

[6]  Anish Arora,et al.  Distributed Reset (Extended Abstract) , 1990, FSTTCS.

[7]  Baruch Awerbuch,et al.  Dynamic networks are as fast as static networks , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[8]  Richard Bellman,et al.  ON A ROUTING PROBLEM , 1958 .

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

[10]  Nancy A. Lynch,et al.  An Upper and Lower Bound for Clock Synchronization , 1984, Inf. Control..

[11]  Boaz Patt-Shamir,et al.  Adapting to asynchronous dynamic networks (extended abstract) , 1992, STOC '92.

[12]  Anish Arora,et al.  Distributed Reset , 1994, IEEE Trans. Computers.

[13]  Eugene Outley Self-stabilizing network protocols , 1992 .

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

[15]  David Peleg,et al.  An optimal synchronizer for the hypercube , 1987, PODC '87.

[16]  Baruch Awerbuch,et al.  Network synchronization with polylogarithmic overhead , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[17]  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.

[18]  Edsger W. Dijkstra,et al.  Self stabilization in spite of distributed control , 1974 .

[19]  Robert G. Gallager,et al.  Broadcasting Topology Information in Computer Networks , 1987 .

[20]  Baruch Awerbuch,et al.  Complexity of network synchronization , 1985, JACM.