Abstract
The multiprocessor job scheduling problem has received considerable attention recently. An extensive list of approximation algorithms has been developed and studied for the problem under a variety of constraints. In this paper, we show that from the viewpoint of approximability, the general multiprocessor job scheduling problem has a very rich structures such that by putting simple constraints on the number of processors in the system, we can obtain four versions of the problem, which are NP-hard with a fully polynomial time approximation scheme, strongly NP-hard with a polynomial time approximation scheme, APX-complete (thus with a constant approximation ratio in polynomial time), and with no constant approximation ratio in polynomial time, respectively.
Supported in part by the National Science Foundation under Grant CCR-0000206.
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References
P. Alimonti, AND V. Kann, Hardenss of approximating problems in cubic graphs, Proc. 34d. Italian Conf. on Algorithms and Complexity, Lecture Notes in Computer Science 1203, Springer-Verlag, pp. 288–298.
A. K. Amoura, E. Bampis, C. Kenyon, AND Y. Manoussakis, Scheduling independent multiprocessor tasks, Proceedings of the 5th Annual European Symposium, Graz, Austria, 1997, pp. 1–12.
S. Arora, C. Lund, R. Motwani, M. Sudan, AND M. Szegedy, Proof verification and hardness of approximation problems, Proceedings of the 33rd Annual IEEE Symposium on Foundations of Comput. Sci., IEEE Computer Society, New York, NY, 1992, pp. 14–23.
M. Bellare, O. Goldreich, AND M. Sudan, Free bits, PCPs and non-approximability-towards tight results, Proceedings of the 36th Annual IEEE Symposium on Foundations of Comput. Sci., IEEE Computer Society, New York, NY, 1995, pp. 422–431.
L. Bianco, P. Dell’Olmo, AND M. G. Speranza, Nonpreemptive scheduling of independent tasks with prespecified processor allocations, Naval Res. Logis., 41 (1994), pp. 959–971.
L. Bianco, J. Blazewicz, P. Dell’Olmo, AND M. Drozdowski, Scheduling preemptive multiprocessor tasks on dedicated processors, Performance Evaluation, 20 (1994), pp. 361–371.
L. Bianco, J. Blazewicz, P. Dell’Olmo, AND M. Drozdowski, Scheduling multiprocessor tasks on a dynamic configuration of dedicated processors, Annals of Operations Research, 58 (1995), pp. 493–517.
L. Bianco, P. Dell’Olmo, AND M.G. Speranza, Scheduling independent tasks with multiple modes, Discrete Appl. Math., 62 (1995), pp. 35–50.
J. Blazewicz, M. Drabowski, AND J. Weglarz, Scheduling multiprocessor tasks to minimize schedule length, IEEE Trans. Comput., C-35 (1986), pp. 389–393.
J. Blazewicz, P. Dell’Olmo, M. Drozdowski, AND M. G. Speranza, Scheduling multiprocessor tasks on three dedicated processors, Inform. Process. Lett., 41 (1992), pp. 275–280.
J. Blazewicz, P. Dell’Olmo, M. Drozdowski, AND M. Speranza, Corrigendum to “Scheduling multiprocessor tasks on three dedicated processors, Inform. Process. Lett., 41 (1992), pp. 275-280”, Inform. Process. Lett., 49 (1994), pp. 269–270.
J. Blazewicz, M. Drozdowski, AND J. Weglarz, Scheduling multiprocessor tasks-a survey, Microcomputer Applications, 13 (1994), pp. 89–97.
J. Chen, AND J. Huang, Semi-normal schedulings: improvement on Goemans’ algorithm, The 9th Annual International Symposium on Algorithms and Computation (ISAAC’01), Lecture Notes in Computer Science 2223, pp. 48–60, 2001.
J. Chen, AND C.-Y. Lee, General multiprocessor task scheduling, Naval Res. Logistics 46, pp. 57–74, 1999.
J. Chen, AND A. Miranda, A polynomial time approximation scheme for general multiprocessor job scheduling, SIAM Journal on Computing, 31 (2001), No. 1, pp. 1–17.
P. Crescenzi, AND L. Trevisan, On approximation scheme preserving reducibil-ity and its applications, Proceedings of the 14th Annual Conf. on Foundations of Software Tech. and Theoret. Comp. Sci., in Lecture Notes in Comput. Sci. 880, Springer-Verlag, Berlin, Germany, 1994, pp. 330–341.
P. Dell’Olmo, AND M. G. Speranza, Graph models for multiprocessor scheduling problems with precedence constraints, Foundation of Computing and Decisions Sciences, 21 (1996), pp. 17–29.
M. Garey, AND D. Johnson, Computers and Intractability, A Guide to the Theory of NP-Completeness, W.H. Freeman and Company, San Francisco, CA, 1979.
M. X. Goemans, An approximation algorithm for scheduling on three dedicated machines, Discrete Appl. Math., 61 (1995), pp. 49–59.
M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, NY, 1980.
J. A. Hoogeveen, S. L. VAN DE Velde, AND B. Veltman, Complexity of scheduling multiprocessor tasks with prespecified processor allocations, Discrete Appl. Math., 55 (1994), pp. 259–272.
J. Huang, J. Chen, AND S. Chen, A simple linear time approximation algorithm for multi-processor job scheduling on four processors, Proceedings of the 8th Annual International Symposium on Algorithms and Computation (ISAAC’00), Lecture Notes in Computer Science 1969, pp. 60–71, 2000.
R. M. Karp, Reducibility among combinatorial problems, in R.E. Miller AND J. W. Thatcher, ed., Complexity of Computer Computations, Plenum Press, New York, 1972, pp. 85–103.
M. Kubale, The complexity of scheduling independent two-processor tasks on dedicated processors, Inform. Process. Lett. (1985), pp. 141–147.
C. H. Papadimitriou, AND M. Yannakakis, Optimization, approximation, and complexity classes, Proceedings of the 20th Annual ACM Symposium on the Theory of Computing, ACM, New York, NY 1988, pp. 229–234.
B. Veltman, B. J. Lageweg, AND J. K. Lenstra, Multiprocessor scheduling with communication delays, Parallel Computing, 16 (1990), pp. 173–182.
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Miranda, A., Torres, L., Chen, J. (2002). On the Approximability of Multiprocessor Task Scheduling Problems. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_36
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DOI: https://doi.org/10.1007/3-540-36136-7_36
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