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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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)
Aggarwal, G., Motwani, R., Zhu, A.: The load rebalancing problem. In: Symposium on Parallel Algorithms and Architectures, pp. 258–265 (2003)
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)
Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. American Elsevier, New York (1977)
Gandhi, R., Mestre, J.: Combinatorial algorithms for data migration to minimize average completion time. Algorithmica 54(1), 54–71 (2009)
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)
Golubchik, L., Khuller, S., Kim, Y., Shargorodskaya, S., Wan, Y.: Data migration on parallel disks: algorithms and evaluation. Algorithmica 45(1), 137–158 (2006)
Graham, R.L., Grahamt, R.L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 416–429 (1969)
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)
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)
Kashyap, S., Khuller, S.: Algorithms for non-uniform size data placement on parallel disks. J. Algorithms 60(2), 144–167 (2006)
Kashyap, S., Khuller, S., Wan, Y.C., Golubchik, L.: Fast reconfiguration of data placement in parallel disks. In: 2006 ALENEX Conference, Jan. 2006
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)
Khuller, S., Kim, Y.A., Wan, Y.C.: Algorithms for data migration with cloning. SIAM J. Comput. 33(2), 448–461 (2004)
Kim, Y.: Data migration to minimize the average completion time. In: Proc. of ACM-SIAM Symposium on Discrete Algorithms, pp. 97–98 (2003)
Meyerson, A., Munagala, K., Plotkin, S.A.: Web caching using access statistics. In: Symposium on Discrete Algorithms, pp. 354–363 (2001)
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)
Shachnai, H., Tamir, T.: On two class-constrained versions of the multiple knapsack problem. Algorithmica 29, 442–467 (2001)
Shannon, C.E.: A theorem on colouring lines of a network. J. Math. Phys. 28, 148–151 (1949)
Shmoys, D.B., Tardos, E.: An approximation algorithm for the generalized assignment problem. Math. Program., Ser. A 62, 461–474 (1993)
Vizing, V.G.: On an estimate of the chromatic class of a p-graph. Diskretn. Anal. 3, 25–30 (1964) (Russian)
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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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DOI: https://doi.org/10.1007/s00453-011-9534-1