Abstract
We will consider a quadratic variant of online scheduling with machine cost. Here, we have a sequence of independent jobs with positive sizes. Jobs come one by one and we have to assign them irrevocably to a machine without any knowledge about additional jobs that may follow later on. Owing to this, the algorithm has no machine at first. When a job arrives, we have the option to purchase a new machine and the cost of purchasing a machine is a fixed constant. In previous studies, the objective was to minimize the sum of the makespan and the cost of the purchased machines. Now, we minimize the sum of squares of loads of the machines and the cost paid to purchase them and we will prove that 4/3 is a general lower bound. After this, we will present a 4/3-competitive algorithm with a detailed competitive analysis.
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Dósa, Gy., He, Y.: Better online algorithms for scheduling with machine cost. SIAM J. Comput. 33(5), 1035–1051 (2004)
Dósa, Gy., He, Y.: Scheduling with machine cost and rejection. J. Comb. Optim. 12(4), 337–350 (2006)
Dósa, Gy., Imreh, Cs.: The generalization of scheduling with machine cost. Theoret. Comput. Sci. 510, 102–110 (2013)
Dósa, Gy., Tan, Z.: New upper and lower bounds for online scheduling with machine cost. Discrete Optim. 7(3), 125–135 (2010)
Han, S., Jiang, Y., Hu, J.: Online algorithms for scheduling with machine activation cost on two uniform machines. J. Zhejiang Univ.-Sci. A 8(1), 127–133 (2007)
He, Y., Cai, S.: Semi-online scheduling with machine cost. J. Comput. Sci. Technol. 17(6), 781–787 (2002)
Imreh, Cs.: Online scheduling with general machine cost functions. Discrete Appl. Math. 157(9), 2070–2077 (2009)
Imreh, C., Noga, J.: Scheduling with machine cost. In: Hochbaum, D.S., Jansen, K., Rolim, J.D.P., Sinclair, A. (eds.) APPROX/RANDOM -1999. LNCS, vol. 1671, pp. 168–176. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-540-48413-4_18
Nagy-György, J., Imreh, Cs.: Online scheduling with machine cost and rejection. Discrete Appl. Math. 155(18), 2546–2554 (2007)
Szwarc, W., Mukhopadhyay, S.K.: Minimizing a quadratic cost function of waiting times in single-machine scheduling. J. Oper. Res. Soc. 46(6), 753–761 (1995)
Townsend, W.: The single machine problem with quadratic penalty function of completion times: a branch-and-bound solution. Manage. Sci. 24(5), 530–534 (1978)
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Csirik, J., Dósa, G., Kószó, D. (2020). Online Scheduling with Machine Cost and a Quadratic Objective Function. In: Chatzigeorgiou, A., et al. SOFSEM 2020: Theory and Practice of Computer Science. SOFSEM 2020. Lecture Notes in Computer Science(), vol 12011. Springer, Cham. https://doi.org/10.1007/978-3-030-38919-2_17
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DOI: https://doi.org/10.1007/978-3-030-38919-2_17
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