Executing Divisible Jobs on a Network with a Fixed Number of Processors
In real practice, a job sometimes can be divided into s independent tasks to be distributed for execution on a network with a fixed number of processors. The overall finish time can vary widely depending on variables such as latency, data partitioning and/or data combining times, the individual execution times, the amount of data to be transferred, and the sending out of more tasks than needed. This paper studies the problem of finding an optimal task scheduling for a divisible job such that the overall finish time is minimized.
We first prove the studied problem is NP-complete and give a simple 3-OPT approximation algorithm. Then we develop a (2 + ε)-OPT linear-time approximation algorithm by generalizing our simple algorithm, where ε is an arbitrarily small constant. A linear-time 2-OPT approximation algorithm is given when we divide the tasks evenly. Algorithms to find optimal solutions are then given for two special cases: 1) when the network has exactly two processors and 2) when the evenly divided tasks have symmetric behaviors. These cases happen frequently in real practice.
KeywordsExecution Time Approximation Algorithm Optimal Schedule Precedence Constraint Communication Time
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- 2.J. Bĺażewicz, K. H. Ecker, E. Pesch, G. Schmidt, and J. Weglarz. Scheduling Computer and Manufacturing Processes. Springer, 1996.Google Scholar
- 5.P. Chrétienne, E. G. Coffman, Jr., J. K. Lenstra, and Z. Liu, editors. Scheduling Theory and its Applications. John Wiley & Sons Ltd, 1995.Google Scholar
- 7.M. R. Garey and D. S. Johnson. COMPUTERS AND INTRACTABILITY A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York, 1979.Google Scholar
- 8.A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Manchek, and V. Sunderam. PVM 3 User’s Guide and Reference Manual. Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA, May 1993.Google Scholar
- 12.T.-s. Hsu and D. R. Lopez. Bounds and algorithms for a practical task allocation model (extended abstract). In Proceedings of 7th International Symposium on Algorithms and Computation, volume LNCS #1178, pages 397–406. Springer-Verlag, 1996.Google Scholar
- 13.V. M. Lo. Task Assignment in Distributed Systems. PhD thesis, Univ. of Illinois at Urbana-Champaign, USA, October 1983.Google Scholar
- 14.D. R. Lopez. Models and Algorithms for Task Allocation in a Parallel Environment. PhD thesis, Texas A&M University, Texas, USA, December 1992.Google Scholar