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Approximately Uniform Online Checkpointing with Bounded Memory

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Abstract

In many complex computational processes one may want to store a sample of the process’ history for later use by placing checkpoints. In this paper we consider the problem of maintaining, in an online fashion, a collection of k checkpoints as an approximately uniformly spaced sample in the history of a continuous-time process. We present deterministic algorithms tailored for small values of k and a general one for arbitrary k. The algorithms are proven to be close to optimum for several different measures.

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References

  1. Asano, T.: Online uniformity of integer points on a line. Inf. Process. Lett. 109, 57–60 (2008). doi:10.1016/j.ipl.2008.09.008

    Article  MathSciNet  Google Scholar 

  2. Babcock, B., Babu, S., Datar, M., Motwani, R., Widom, J.: Models and issues in data stream systems. In: Proc. 21st ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS 2002), pp. 1–16. ACM, New York (2002). doi:10.1145/543613.543615

    Google Scholar 

  3. Benary, J.: Parallelism in the reverse mode. In: Computational Differentiation: Techniques, Applications, and Tools. Proceedings in Applied Mathematics. SIAM, Philadelphia (1996)

    Google Scholar 

  4. Berggren, M.: Numerical solution of a flow-control problem: vorticity reduction by dynamic boundary action. SIAM J. Sci. Comput. 19, 829–860 (1998). doi:10.1137/S1064827595294678

    Article  MathSciNet  MATH  Google Scholar 

  5. Bern, M., Greene, D.H., Raghunathan, A., Sudan, M.: On-line algorithms for locating checkpoints. Algorithmica 11, 33–52 (1994). doi:10.1007/BF01294262

    Article  MathSciNet  MATH  Google Scholar 

  6. Chazelle, B.: The Discrepancy Method: Randomness and Complexity. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  7. Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. Dover, New York (2006)

    Google Scholar 

  8. Muthukrishnan, S.: Data streams: algorithms and applications. Found. Trends Theor. Comput. Sci. 1, 117–236 (2005)

    Article  MathSciNet  Google Scholar 

  9. Nicola, V., van Spanje, J.: Comparative analysis of different models of checkpointing and recovery. IEEE Trans. Softw. Eng. 16, 807–821 (1990). doi:10.1109/32.57620

    Article  Google Scholar 

  10. Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (1992)

    Book  MATH  Google Scholar 

  11. Stumm, P., Walther, A.: Multistage approaches for optimal offline checkpointing. SIAM J. Sci. Comput. 31, 1946–1967 (2009). doi:10.1137/080718036

    Article  MathSciNet  MATH  Google Scholar 

  12. Stumm, P., Walther, A.: New algorithms for optimal online checkpointing. SIAM J. Sci. Comput. 32, 836–854 (2010). doi:10.1137/080742439

    Article  MathSciNet  MATH  Google Scholar 

  13. Teramoto, S., Asano, T., Doerr, B., Katoh, N.: Inserting points uniformly at every instance. IEICE Trans. Inf. Syst. 89-D, 2348–2356 (2006). doi:10.1093/ietisy/e89-d.8.2348

    Article  Google Scholar 

  14. van der Corput, J.G.: Verteilungsfunktionen. Proc. K. Ned. Akad. Wet. 38, 813–821 (1935)

    Google Scholar 

  15. Walther, A.: Bounding the number of processors and checkpoints needed in time-minimal parallel reversal schedules. Computing 73, 135–154 (2004). doi:10.1007/s00607-004-0075-1

    MathSciNet  MATH  Google Scholar 

  16. Ziv, A., Bruck, J.: An on-line algorithm for checkpoint placement. IEEE Trans. Comput. 46, 976–985 (1997). doi:10.1009/12.620479

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors are thankful to Pekka Orponen for some helpful comments. L.A. has been supported by the Helsinki Graduate School in Computer Science and the Nokia Foundation.

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Correspondence to Lauri Ahlroth.

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This research has been supported by the Academy of Finland under grant 128823. The third author has also been supported by the Cloud Software Programme of the Finnish Strategic Centre for Science, Technology and Innovation in ICT, TiViT. The main progress of the paper has been done while the second author was affiliated with Aalto University, Department of Information and Computer Science. A preliminary version of this work appeared in the 17th Annual International Computing and Combinatorics Conference, Dallas, Texas, USA, 2011.

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Ahlroth, L., Pottonen, O. & Schumacher, A. Approximately Uniform Online Checkpointing with Bounded Memory. Algorithmica 67, 234–246 (2013). https://doi.org/10.1007/s00453-013-9772-5

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