Abstract
In this paper, we consider the scheduling with rejection. The objective functions are to minimize the maximum completion time of the processed ones when the total compression cost is given. Firstly, we prove that the problem 1|rej| C max /TCP is NP-hard, which implying that P m |rej| C max /TCP, 1 |rej, r j |C max /TCP, 1 |rej, on − line|C max /TCP are all NP-hard. Secondly, for problem P m |rej| C max /TCP, we design a pseudopolynomial time dynamic programming algorithm that solves it exactly and an FPTAS (full polynomial time approximation scheme) when m is a constant. We also design a pseudopolynomial time dynamic programming algorithm and an FPTAS for the case of non-identical job arrival problem 1 |rej, r j |C max /TCP. In the end, we consider the on-line problem 1 |rej, on − line|C max /TCP and prove that there doesn’t exist any on-line algorithm with a constant competitive ratio for it, even if the jobs only have two different release times.
Supported by the National Natural Science Foundation(Grant Number 10671108) and the Province Natural Science Foundation of Shandong (Grant Number Y2005A04).
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Afrati, F., Bampis, E., Chekuri, C., Karger, D., Kenyon, C., Khanna, S., Milis, I., Queyranne, M., Skutella, M., Stein, C., Sviridenko, M.: Approximation Schemes for Minimizing Average Weighted Completion Time with Release Data. In: Proceedings of 40th FOCS, pp. 32–43 (1999)
Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., Stougie, L.: Multi-Processor Scheduling with Rejection. SIAM Journal of Discrete Maths. 13, 64–78 (2000)
Cao, Z., Zhang, Y.: Scheduling with Rejection and Non-Identical Job Arrivals. Journal of System Science and Complexity 20, 529–535 (2007)
Engels, D.W., Karger, D.R., Kolliopoulos, S.G., Sengupta, S., Uma, R.N., Wein, J.: Techniques for Scheduling with Rejection. Journal of Algorithms 49(1), 175–191 (2003)
Epstein, L., Noga, J., Woeginger, G.J.: On-line Scheduling of Unit Time Jobs with Rejection: Minimizing the Total Completion Time. Operations Research Letters 30, 415–420 (2002)
Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and Approximation in Deterministic Sequencing and Scheduling: A Survey. Ann. Disc. Math. 5, 287–326 (1979)
He, Y., Min, X.: On-Line Uniform Machine Scheduling with Rejection. Computing 65, 1–12 (2000)
Seiden, S.S.: Preemptive Multiprocessor Scheduling with Rejection. Theoretical Computer Science 262, 437–458 (2001)
Sengupta, S.: Algorithms and Approximation Schemes for Minimizing Lateness/Tardiness Scheduling with Rejection. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 79–90. Springer, Heidelberg (2003)
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Zhang, Y., Ren, J., Wang, C. (2009). Scheduling with Rejection to Minimize the Makespan. In: Du, DZ., Hu, X., Pardalos, P.M. (eds) Combinatorial Optimization and Applications. COCOA 2009. Lecture Notes in Computer Science, vol 5573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02026-1_39
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DOI: https://doi.org/10.1007/978-3-642-02026-1_39
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