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Improved Approximation Algorithms for Data Migration

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Abstract

Our work is motivated by the need to manage data items on a collection of storage devices to handle dynamically changing demand. As demand for data items changes, for performance reasons, the system needs to automatically respond to changes in demand for different data items. The problem of computing a migration plan among the storage devices is called the data migration problem. This problem was shown to be NP-hard, and an approximation algorithm achieving an approximation factor of 9.5 was presented for the half-duplex communication model in Khuller, Kim and Wan (Algorithms for data migration with cloning. SIAM J. Comput. 33(2):448–461, 2004). In this paper we develop an improved approximation algorithm that gives a bound of 6.5+o(1) using new ideas. In addition, we develop better algorithms using external disks and get an approximation factor of 4.5 using external disks. We also consider the full duplex communication model and develop an improved bound of 4+o(1) for this model, with no external disks.

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References

  1. Anderson, E., Hall, J., Hartline, J., Hobbes, M., Karlin, A., Saia, J., Swaminathan, R., Wilkes, J.: An experimental study of data migration algorithms. In: Workshop on Algorithm Engineering, London, UK, 2001, pp. 145–158. Springer, Berlin (2001)

    Chapter  Google Scholar 

  2. Aggarwal, G., Motwani, R., Zhu, A.: The load rebalancing problem. In: Symposium on Parallel Algorithms and Architectures, pp. 258–265 (2003)

    Google Scholar 

  3. Baev, I.D., Rajaraman, R.: Approximation algorithms for data placement in arbitrary networks. In: Proc. of ACM-SIAM Symposium on Discrete Algorithms, pp. 661–670 (2001)

    Google Scholar 

  4. Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. American Elsevier, New York (1977)

    Google Scholar 

  5. Gandhi, R., Mestre, J.: Combinatorial algorithms for data migration to minimize average completion time. Algorithmica 54(1), 54–71 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Golubchik, L., Khanna, S., Khuller, S., Thurimella, R., Zhu, A.: Approximation algorithms for data placement on parallel disks. In: Proc. of ACM-SIAM Symposium on Discrete Algorithms, Washington, D.C., USA, 2000, pp. 661–670. Society of Industrial and Applied Mathematics, Philadelphia (2000)

    Google Scholar 

  7. Golubchik, L., Khuller, S., Kim, Y., Shargorodskaya, S., Wan, Y.: Data migration on parallel disks: algorithms and evaluation. Algorithmica 45(1), 137–158 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Graham, R.L., Grahamt, R.L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 416–429 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  9. Guha, S., Munagala, K.: Improved algorithms for the data placement problem, 2002. In: Proc. of ACM-SIAM Symposium on Discrete Algorithms, San Fransisco, CA, USA, 2002, pp. 106–107. Society of Industrial and Applied Mathematics, Philadelphia (2002)

    Google Scholar 

  10. Hall, J., Hartline, J., Karlin, A., Saia, J., Wilkes, J.: On algorithms for efficient data migration. In: Proc. of ACM-SIAM Symposium on Discrete Algorithms, pp. 620–629 (2001)

    Google Scholar 

  11. Kashyap, S., Khuller, S.: Algorithms for non-uniform size data placement on parallel disks. J. Algorithms 60(2), 144–167 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kashyap, S., Khuller, S., Wan, Y.C., Golubchik, L.: Fast reconfiguration of data placement in parallel disks. In: 2006 ALENEX Conference, Jan. 2006

    Google Scholar 

  13. Khuller, S., Kim, Y., Wan, Y.C.: On generalized gossiping and broadcasting. In: European Symposia on Algorithms, Budapest, Hungary, 2003, pp. 373–384. Springer, Berlin (2003)

    Google Scholar 

  14. Khuller, S., Kim, Y.A., Wan, Y.C.: Algorithms for data migration with cloning. SIAM J. Comput. 33(2), 448–461 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kim, Y.: Data migration to minimize the average completion time. In: Proc. of ACM-SIAM Symposium on Discrete Algorithms, pp. 97–98 (2003)

    Google Scholar 

  16. Meyerson, A., Munagala, K., Plotkin, S.A.: Web caching using access statistics. In: Symposium on Discrete Algorithms, pp. 354–363 (2001)

    Google Scholar 

  17. Shachnai, H., Tamir, T.: Polynomial time approximation schemes for class-constrained packing problems. In: Workshop on Approximation Algorithms. LNCS, vol. 1913, pp. 238–249 (2000)

    Google Scholar 

  18. Shachnai, H., Tamir, T.: On two class-constrained versions of the multiple knapsack problem. Algorithmica 29, 442–467 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  19. Shannon, C.E.: A theorem on colouring lines of a network. J. Math. Phys. 28, 148–151 (1949)

    MathSciNet  MATH  Google Scholar 

  20. Shmoys, D.B., Tardos, E.: An approximation algorithm for the generalized assignment problem. Math. Program., Ser. A 62, 461–474 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  21. Vizing, V.G.: On an estimate of the chromatic class of a p-graph. Diskretn. Anal. 3, 25–30 (1964) (Russian)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Maryland, College Park, MD, 20742, USA

    Samir Khuller & Azarakhsh Malekian

  2. Department of Computer Science and Engineering, University of Connecticut, Storrs, CT, 06269, USA

    Yoo-Ah Kim

Authors
  1. Samir Khuller
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  2. Yoo-Ah Kim
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  3. Azarakhsh Malekian
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Corresponding author

Correspondence to Azarakhsh Malekian.

Additional information

A preliminary version of the paper was presented at the 2006 APPROX conference.

Research of S. Khuller was supported by NSF CCF 0728839 and a Google Research Award.

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Khuller, S., Kim, YA. & Malekian, A. Improved Approximation Algorithms for Data Migration. Algorithmica 63, 347–362 (2012). https://doi.org/10.1007/s00453-011-9534-1

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