Abstract
In this paper, we analyze network recovery algorithms, which allow computer networks to properly function in spite of failures. In this analysis, we use methods and tools of the theory of super-recursive algorithms. The concept of algorithm of the second level is introduced and studied. It is demonstrated that although the main components of various check-point/recovery algorithms are recursive algorithms, check-point/recovery algorithms, as a whole, are super-recursive second-level algorithms. Treating network recovery algorithms as second level algorithms is oriented at developing more powerful algorithms by combining existing ones in a common schema.
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References
Blum, L., Cucker, F., Shub, M., Smale, S.: Complexity of Real Computation. Springer, New York (1998)
Burgin, M.: Nonlinear phenomena in spaces of algorithms. Int. J. Comput. Math. 80(12), 1449–1476 (2003)
Burgin, M.: Superrecursive Algorithms. Springer, New York (2005)
Cao, G., Singhal, M.: Mutable Checkpoints: A new checkpointing approach for mobile computing systems. IEEE Trans. Parallel Distrib. Syst. 12(2), 157–172 (2001)
Codd, E.F.: Cellular Automata. Academic Press, New York (1968)
Elnozahy, E.N., Johnson, D.B., Zwaenepoel, W.: The performance of consistent check pointing. In: Proceedings of the 11th Symp. Reliable Distributed Systems, pp. 86–95 (1992)
Gupta, B., Rahimi, S.: Novel crash recovery approach for concurrent failures in cluster federation. In: Lecture Notes in Computer Science, vol. 5529, pp. 434–445 (2009)
Gupta, B., Rahimi, S., Liu, Z.: A novel low-overhead roll-forward recovery scheme for distributed systems. IET Comput. Digit. Tech. 1(4), 397–404 (2007)
Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Boston (2007)
Manivannan, D., Singhal, M.: Asynchronous recovery without using vector timestamps. J. Parallel Distrib. Comput. 62, 1695–1728 (2002)
Koo, R., Toueg, S.: Checkpointing and rollback-recovery for distributed systems. IEEE Trans. Softw. Eng. SE-13(1), 23–31 (1987)
Miller, M.: Cloud Computing: Web-Based Applications that Change the Way You Work and Collaborate Online. Safari (2008)
Rogers, H.: Theory of Recursive Functions and Effective Computability. MIT Press, Cambridge (1987)
Sipser, M.: Introduction to the Theory of Computation. PWS Publishing, Boston (1997)
Van Leeuwen, J., Wiedermann, J.: On the power of interactive computing. In: Proceedings of the IFIP Theoretical Computer Science, pp. 619–623 (2000)
Knuth, D.: The Art of Computer Programming, Vol. 1: Fundamental Algorithms. Addison-Wesley, Reading (1973)
Burgin, M.: Algorithmic control in concurrent computations. In: Proceedings of the 2006 International Conference on Foundations of Computer Science, pp. 17–23. CSREA Press, Las Vegas (2006)
Lewis, J.P.: Limits to software estimation. Softw. Eng. Notes 26(4), 54–59 (2001)
Burgin, M.: Measuring Power of Algorithms, Computer Programs, and Information Automata. Nova Science Publishers, Hauppauge (2010)
Chandy, K.M., Lamport, L.: Distributed snapshots: determining global states of distributed systems. ACM Trans. Comput. Syst. 3(1), 63–75 (1985)
Manivannan, D., Singhal, M.: Quasi-synchronous checkpointing: models, characterization, and classification. IEEE Trans. Parallel Distrib. Syst. 10(7), 703–713 (1999)
Randell, B.: Reliable Computing Systems, Operating Systems: An Advanced Course, pp. 282–391. Springer, New York (1979)
Netzer, R.H.B., Xu, J.: Necessary and sufficient conditions for consistent global snapshots. IEEE Trans. Parallel Distrib. Syst. 6(2), 165–169 (1995)
Briatico, D., Ciuffoletti, A., Simoncini, L.: A distributed domino-effect free recovery algorithm. In: Proceedings of the 4th IEEE Symposium on Reliability in Distributed Software and Database, pp. 207–215 (1984)
Cao, G., Singhal, M.: Checkpointing with mutable checkpoints. Theor. Comput. Sci. 290, 1127–1148 (2003)
Silva, L.M.E., Silva, J.G.: Global checkpointing for distributed programs. In: Proceedings of the 11th IEEE Symposium on Reliable Distributed Systems, pp. 155–162 (1992)
Lamport, L.: Time, clocks, and the ordering of events in a distributed system. Commun. ACM 21(7), 558–565 (1978)
Gupta, B., Nikolaev, R., Chirra, R.: A recovery scheme for cluster federations using sender-based message logging, to appear in the J. Comput. Inf. Technol.
Cao, J., Chen, Y., Zhang, K., He, Y.: Checkpointing in hybrid distributed systems. In: Proceedings of 7th Intl. Symposium on Parallel Architectures, Algorithms and Networks (ISPAN’04), Hong Kong, China, pp. 136–141 (2004)
Monnet, S., et al.: Hybrid checkpointing for parallel applications in cluster federations. In: Proceedings of 4th IEEE/ACM Intl. Symposium on Cluster Computing and the Grid, Chicago, USA, pp. 773–782 (2004)
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Burgin, M., Gupta, B. Second-Level Algorithms, Superrecursivity, and Recovery Problem in Distributed Systems. Theory Comput Syst 50, 694–705 (2012). https://doi.org/10.1007/s00224-011-9369-9
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DOI: https://doi.org/10.1007/s00224-011-9369-9