Abstract
We consider the problem of scheduling n independent multiprocessor tasks with due dates and unit processing times, where the objective is to compute a schedule maximizing the throughput. We derive the complexity results and present several approximation algorithms. For the parallel variant of the problem, we introduce the first-fit increasing algorithm and the latest-fit increasing algorithm, and prove that their worst-case ratios are 2 and 2 − 1/m, respectively (m ≥ 2 is the number of processors). Then we propose a revised algorithm with worst-case ratio bounded by 3/2 − 1/(2m − 2) (m is even) and 3/2 − 1/(2m) (m is odd). For the dedicated variant, we present a simple greedy algorithm. We show that its worst-case ratio is bounded by √m+ 1. We straighten this result by showing that the problem (even for a common due date D = 1) cannot be approximated within a factor of m 1/2−ε for any ε > 0, unless NP = ZPP.
Supported by Alexander von Humboldt Foundation.
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References
F. Afrati, E. Bampis, A.V. Fishkin, K. Jansen, and C. Kenyon. Scheduling to minimize the average completion time of dedicated tasks. In Proceedings 20th Conference on Foundations of Software Technology and Theoretical Computer Science, LNCS 1974, pages 454–464. Springer Verlag, 2000.
P. Brucker. Scheduling Algorithms. Springer Verlag, 1998.
X. Cai, C.-Y. Lee, and C.-L. Li. Minimizing total completion time in two-processor task systems with prespecified processor allocation. Naval Research Logistics, 45:231–242, 1998.
E.G. Coffman, J.Y-T. Leung, and D.W. Ting. Bin packing: maximizing the number of pieces packed. Acta Informatica, 9:263–271, 1978.
M. Drozdowski. Scheduling multiprocessor tasks-an overview. European Journal of Operational Research, 94:215–230, 1996.
A. Feldmann, J. Sgall, and S.-H. Teng. Dynamic scheduling on parallel machines. Theoretical Computer Science, 130:49–72, 1994.
A.V. Fishkin and K. Jansen, and L. Porkolab. On minimizing average weighted completion time of multiprocessor tasks with release dates. In Proceedings 28th International Colloquium on Automata, Languages and Programming, LNCS 2076, pages 875–886. Springer Verlag, 2001.
M.R. Garey and D.S. Johnson. Computers and intractability: A guide to the theory of NP-completeness. Freeman, San Francisco, CA, 1979.
R.L. Graham, E.L. Lawler, J.K. Lenstra, and A.H.G. Rinnooy Kan. Optimization and approximation in deterministic scheduling: a survey. Annals of Discrete Mathematics, 5:287–326, 1979.
J. Hastad. Clique is hard to approximate within n1−ε. Acta Mathematica, 182:105–142, 1999.
J.A. Hoogeveen, S.L. Van de Velde, and B. Veltman. Complexity of scheduling multiprocessor tasks with prespecified processor allocations. Discrete Applied Mathematics, 55:259–272, 1994.
H. Kellerer. A polynomial time approximation scheme for the multiple knapsack problem. RANDOM-APPROX, pages 51–62, 1999.
E.L. Lawler. Sequencing to minimize the weighted number of of tardy jobs. RAIRO Recherche opérationnele, S10:27–33, 1976.
E.L. Lloyd. Concurrent task systems. Operations Research, 29:189–201, 1981.
C.L. Monma. Linear-time algorithms for scheduling on parallel processors. Operation Research, 37:116–124, 1982.
J. Turek, W. Ludwig, J. Wolf, and P. Yu. Scheduling parallel tasks to minimize average response times. In Proceedings 5th ACM-SIAM Symposium on Discrete Algorithms, pages 112–121, 1994.
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Fishkin, A.V., Zhang, G. (2002). On Maximizing the Throughput of Multiprocessor Tasks. In: Diks, K., Rytter, W. (eds) Mathematical Foundations of Computer Science 2002. MFCS 2002. Lecture Notes in Computer Science, vol 2420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45687-2_22
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DOI: https://doi.org/10.1007/3-540-45687-2_22
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