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Data migration to minimize the total completion time

Published: 01 April 2005 Publication History

Abstract

We consider the data migration problem, which is the problem of finding an efficient schedule to migrate data in a network. The data layout of a large storage server needs to be computed based on the expected data access pattern for load balancing. As the data access pattern changes over time, we need to recompute a new layout and then migrate the data from its current layout to the new layout. Our objective is to minimize the total completion time over all storage devices. We develop a 3-approximation algorithm when each migration job needs the same amount of time and a 9- approximation when the times required for different migration jobs are different. Another interesting objective is to minimize the total completion time over all data migration jobs. We present a 10- approximation algorithm when each migration job has a different processing time. We extend our results to the resource constrained scheduling problem where each job requires at most m resources. We obtain O(m)-approximations for both resource and job completion times.

References

[1]
{1} E. Anderson, J. Hall, J. Hartline, M. Hobbes, A. Karlin, J. Saia, R. Swaminathan, J. Wilkes, An experimental study of data migration algorithms, Workshop on Algorithm Engineering (2001) 145-158.]]
[2]
{2} A. Bar-Noy, M. Bellare, M.M. Halldórsson, H. Shachnai, T. Tamir, On chromatic sums and distributed resource allocation, Inform. Comput. 140 (1998) 183-202.]]
[3]
{3} A. Bar-Noy, M.M. Halldórsson, G. Korsarz, Tight bound for the sum of a greedy coloring, Inform. Process. Lett. 71 (1999) 135-140.]]
[4]
{4} A. Bar-Noy, M.M. Halldórsson, G. Korsarz, H. Shachnai, R. Salman, Sum multi-coloring of graphs, J. Algorithms 37 (2) (2000) 422-450.]]
[5]
{5} A. Bar-Noy, G. Kortsarz, The minimum color-sum of bipartite graphs, J. Algorithms 28 (1998) 339-365.]]
[6]
{6} A. Caprara, R. Rizzi, Improving a family of approximation algorithms to edge color multi-graphs, Inform. Process. Lett. 68 (1998) 11-15.]]
[7]
{7} E.G. Coffman, M.R. Garey, D.S. Johnson, A.S. Lapaugh, Scheduling file transfers, SIAM J. Comput. 14 (3) (1985) 744-780.]]
[8]
{8} R. Gandhi, M. Halldorsson, G. Kortsarz, H. Shachnai, Improved results for data migration and open-shop scheduling, in: The 31st International Colloquium on Automata, Languages and Programming (ICALP), 2004.]]
[9]
{9} R. Gandhi, M. Halldorsson, G. Kortsarz, H. Shachnai, Improved bounds for sum multicoloring and weighted completion time of dependent jobs, in: Proc. of the Second Workshop on Approximation and Online Algorithms (WAOA), Sept. 2004.]]
[10]
{10} M.K. Goldberg, Edge-coloring of multi-graphs: recoloring technique, J. Graph Theory 8 (1984) 121-137.]]
[11]
{11} L. Golubchik, S. Khanna, S. Khuller, R. Thurimella, A. Zhu, Approximation algorithms for data placement on parallel disks, in: Proc. of the 11th Symposium on Discrete Algorithms, 2000, pp. 223-232.]]
[12]
{12} J. Hall, J. Hartline, A. Karlin, J. Saia, J. Wilkes, On algorithms for efficient data migration, in: Proc. of the 12th Symposium on Discrete Algorithms, 2001, pp. 620-629.]]
[13]
{13} L.A. Hall, A.S. Schulz, D.B. Shmoys, J. Wein, Scheduling to minimize average completion time: off-line and on-line algorithms, Math. Oper. Res. 22 (1997) 513-544.]]
[14]
{14} M.M. Halldórsson, G. Kortsarz, H. Shachani, Minimizing average completion of dedicated tasks and partially ordered sets, in: 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, 2001, pp. 114-126.]]
[15]
{15} D.S. Hochbaum, T. Nishizeki, D.B. Shmoys, A better than "Best Possible" algorithm to edge color multigraphs, J. Algorithms 7 (1986) 79-104.]]
[16]
{16} I. Holyer, The NP-completeness of edge-coloring, SIAM J. Comput. 10 (4) (1981) 718-720.]]
[17]
{17} S. Kashyap, S. Khuller, Algorithms for non-uniform size data placement on parallel disks, in: Foundations of Software Technology and Theoretical Computer Science, 2003.]]
[18]
{18} E. Kubicka, G. Kubicki, D. Kountanis, Approximation algorithms for the chromatic sum, in: Proceedings of the First Great Lakes Computer Science Conference, in: Lecture Notes in Comput. Sci., vol. 1203, Springer-Verlag, Berlin, 1989, pp. 15-21.]]
[19]
{19} S. Nicoloso, M. Sarrafzadeh, X. Song, On the sum coloring problem on interval graphs, Algorithmica 23 (1999) 109-126.]]
[20]
{20} T. Nishizeki, K. Kashiwagi, On the 1.1 edge-coloring of multi-graphs, SIAM J. Discrete Math. 3 (3) (1990) 391-410.]]
[21]
{21} H. Shachnai, T. Tamir, On two class-constrained versions of the multiple knapsack problem, Algorithmica 29 (2001) 442-467.]]
[22]
{22} H. Shachnai, T. Tamir, Polynomial time approximation schemes for class-constrained packing problems, in: Proc. of Workshop on Approximation Algorithms, 2000, pp. 238-249.]]
[23]
{23} V.G. Vizing, On an estimate of the chromatic class of a p-graph, Diskret. Analiz. 3 (1964) 25-30 (in Russian).]]
[24]
{24} M. Queyranne, Structure of a simple scheduling polyhedron, Math. Programming 58 (1993) 263-285.]]

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cover image Journal of Algorithms
Journal of Algorithms  Volume 55, Issue 1
April 2005
98 pages

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Academic Press, Inc.

United States

Publication History

Published: 01 April 2005

Author Tags

  1. approximation algorithms
  2. data migration
  3. linear programming
  4. scheduling

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