Memory-efficient self stabilizing protocols for general networks
A self stabilizing protocol for constructing a rooted spanning tree in an arbitrary asynchronous network of processors that communicate through shared memory is presented. The processors have unique identifiers but are otherwise identical. The network topology is assumed to be dynamic, that is, edges can join or leave the computation before it eventually stabilizes.
The algorithm is design uses a new paradigm in self stabilization. The idea is to ensure that if the system is not in a legal state (this is a global condition) then a local condition of some node will be violated. Thus the new could restart the algorithm.
The algorithm provides an underlying self-stabilization mechanism and can serve as a basic building block in the construction of self stabilizing protocols for several other applications such as: mutual-exclusion, snapshot, and reset.
The algorithm is memory efficient in that it requires only a linear size memory of words of size log n (the size of an identity) over the entire network. Each processor needs a constant number of words per incident link, thus the storage requirement is in the same order of magnitude as the size of the traditionally assumed message buffers size. The adversary may be permitted to initiate the values of the variables to any size. Still, in this case the additional memory used by the algorithm is the amount stated above.
Extensions of our algorithm to other models are also discussed.
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- [AAG87]Y. Afek, B. Awerbuch, and E. Gafni. Applying static network protocols to dynamic networks. In Proc. of the 28th IEEE Annual Symp. on Foundation of Computer Science, pages 358–370, October 1987.Google Scholar
- [AB89]Y. Afek and G. M. Brown. Self-stabilization of the alternating-bit protocol. In Proceedings of the 8th IEEE Symposium on Reliable Distributed Systems, pages 10–12, October 1989.Google Scholar
- [AG90]A. Arora and M. Gouda. Distributed reset. Extended Abstract, 1990.Google Scholar
- [Ang80]D. Angluin. Local and global properties in networks of processes. In Proc. of the 12th Ann. ACM Symp. on Theory of Computing, pages 82–93, May 1980.Google Scholar
- [AM89]Y. Afek, and Y. Matias Simple and Efficient Election Algorithms for Anonymous Networks, 3rd International Workshop on Distributed Algorithms, Nice, France, September 1989.Google Scholar
- [BGW89]G. Brown, M. Gouda, and C.L. Wu. Token systems that self stabilize. IEEE Transactions on Computers, 38(6):845–852, 1989.Google Scholar
- [BP89]J. E. Burns and J Pachl. Uniform self-stabilizing rings. ACM Trans. on Programming Languages and Systems, 11(2):330–344, 1989.Google Scholar
- [Dij74]E. W. Dijkstra. Self-stabilizing systems in spite of distributed control. CACM, 17:643–644, November 1974.Google Scholar
- [DIM90]S. Dolev, A. Israeli, and S. Moran. Self stabilization of dynamic systems assuming read/write atomicity. In Proc. of the ACM Symp. on Principles of Distributed Computing, August 1990.Google Scholar
- [DIM90a]S. Dolev, A. Israeli, and S. Moran. Private communicationGoogle Scholar
- [KP90]Shmuel Katz and Kenneth J. Perry. Self-stabilizing extensions. In Proc. of the ACM Symp. on Principles of Distributed Computing, August 1990.Google Scholar
- [SG89]J. Spinelli and R.G. Gallager. Broadcast topology information in computer networks. IEEE Transactions on Communication, 1989.Google Scholar