Abstract
Refining self-stabilizing algorithms which use tighter schedul- ing constraints (weaker daemon) into corresponding algorithms for weak- er or no scheduling constraints (stronger daemon), while preserving the stabilization property, is useful and challenging. Designing transforma- tion techniques for these refinements has been the subject of serious in- vestigations in recent years. This paper proposes a transformation tech- nique to achieve the above task. The heart of the transformer is a self- stabilizing local mutual exclusion algorithm. The local mutual exclusion problem is to grant a process the privilege to enter the critical section if and only if none of the neighbors of the process has the privilege. The con- tribution of this paper is twofold. First, we present a bounded-memory self-stabilizing local mutual exclusion algorithm for arbitrary network, assuming any arbitrary daemon. After stabilization, this algorithm main- tains a bound on the service time (the delay between two successive ex- ecutions of the critical section by a particular process). This bound is nx(n-1)/2where n is the network size. Second, we use the local mutual ex- clusion algorithm to design two scheduler transformers which convert the algorithms working under a weaker daemon to ones which work under the distributed, arbitrary (or unfair) daemon, both transformers preserv- ing the self-stabilizing property. The first transformer refines algorithms written under the central daemon, while the second transformer refines algorithms designed for the fc-fair (k≥(n - 1)) daemon.
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References
A. Arora and M. Nesterenko. Stabilization-preserving atomicity refinement. DISC’99, pages 254–268, 1999.
B. Awerbuch and M. Saks. A dining philosophers algorithm with polynomial response time. 31st Annual Symposium on Foundations of Computer Science, volume 1:65–74, October 1990.
GH. Antonoiu and P.K. Srimani. Mutual exclusion between neighboring nodes in an arbitrary system graph tree that stabilizes using read/write atomicity. In Euro-par99, Parallel Processing, Proceedings LNCS:1685, pages 823–830, 1999.
V. Barbosa and E. Gafni. Concurrency in heavily loaded neighborhood-constrained systems. Transactions on Programming Languages and Systems Vol 11 Num 4, pages 562–584, 1989.
J.M. Couvreur, N. Francez, and M.G. Gouda. Asynchronous unison. ICD-CS92 Proceedings of the 12th International Conference on Distributed Computing Systems, pages 486–493, 1992.
M. Chandy and J. Misra. The drinking philosophers problem. ACM Transa-tions on Programming Languages and Systems, pages 6(4):632–646, October 1984.
S. Dolev, M. G. Gouda, and M. Schneider. Memory requirements for silent stabilization. In PODC96 Proceedings of the Fifteenth Annual ACM Symposium on Principles of Distributed Computing, pages 27–34, 1996.
E. W. Dijkstra. Hierarchical ordering of sequential processes. Ada Informatica, pages 115–138, 1971.
E. W. Dijkstra. Self-stabilizing systems in spite of distributed control. ACM 17, pages 643–644, 1974.
S. Dolev, A. Israeli, and S. Moran. Self-stabilizing of dynamic systems assuming only read/write atomicity. Distributed Computing, 7:3–16, 1993.
S. Dolev. Self-Stabilization. The MIT Press, 2000.
M. Gouda and F. Hadix. The linear alternator. Proceedings of the third workshop on self-stabilizing systems (WSS-97), International Informatics Series 7, Carleton University Press, pages 31–47, 1997.
M. Gouda and F. Hadix. The alternator. In Proceedings of the Third Workshop on Self-Stabilizing Systems (published in association with ICDCS99 The 19th IEEE International Conference on Distributed Computing Systems), pages 48–53, 1999.
S. Ghosh and Mehmet Hakan Karaata. A self-stabilizing algorithm for coloring planar graphs. Distributed Computing, pages 7:55–59, 1993.
M. G. Gouda. The stabilizing philosopher: asymmetry by memory and by action. Tech Rep TR-87-12, Univesity of Texas at Austin, 1987.
D. Hoover and J. Poole. A distributed self-stabilizing solution for the dining philosophers problem. Information Processing Letter 1 1, pages 209–213, 1989.
S.T. Huang. The fuzzy philoshophers. In Workshop on Advances of Paral-leland Distributed Computational Models, page to appear, May 2000.
C. Johnen, L. O. Alima, A. K. Datta, and S. Tixeuil. Self-stabilizing neighborhood synchronizer in tree networks. In Proceedings of the Nineteenth International Conference on Distributed Computing Systems (ICDCS’99), pages 487–494, June 1999.
M. Mizuno and M. Nesterenko. A transformation of self-stabilizing serial model programs for asynchronous parallel computing environments. Information Processing Letter 66, pages 285–290, 1997.
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Beauquier, J., Datta, A.K., Gradinariu, M., Magniette, F. (2000). Self-Stabilizing Local Mutual Exclusion and Daemon Refinement. In: Herlihy, M. (eds) Distributed Computing. DISC 2000. Lecture Notes in Computer Science, vol 1914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40026-5_15
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DOI: https://doi.org/10.1007/3-540-40026-5_15
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