Abstract
The problem of scheduling independent jobs on m parallel machines in an online fashion was introduced by Graham in 1966. While the deterministic case of this problem has been studied extensively, little work has been done on the randomized case. For m = 2 an algorithm achieving a competitive ratio of 4/3 was found by Bartal, Fiat, Karloff and Vohra. These same authors show a matching lower bound. Chen, van Vliet and Woeginger, and independently Sgall, have shown a lower bound which converges to \(\frac{e}{{e - 1}}\)as m goes to infinity. Prior to this work, no randomized algorithm for m > 2 was known. A randomized algorithm for m ≥ 3 is presented. It achieves competitive ratios of 1.55665, 1.65888, 1.73376, 1.78295 and 1.81681, for m = 3,..., 7 respectively. These competitive ratios are less than the best deterministic lower bound for m = 3, 4, 5 and less than the competitive ratio of the best deterministic algorithm for m < 7.
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References
Albers, S. Better bounds for online scheduling. In Proc. 29th ACM Symposium on Theory of Computing (STOC) (1997), pp. 130–139.
Bartal, Y., Fiat, A., Karloff, H., AND Vohra, R. New algorithms for an ancient scheduling problem. In Proceedings of the Twenty-Fourth Annual ACM Symposium on the Theory of Computing (May 1992), pp. 51–58.
Bartal, Y., Fiat, A., Karloff, H., and Vohra, R. New algorithms for an ancient scheduling problem. Journal of Computer and System Sciences 51, 3 (Dec 1995), 359–366.
Bartal, Y., Karloff, H., and Rabani, Y. A better lower bound for on-line scheduling. Information Processing Letters 50, 3 (May 1994), 113–116.
Chen, B., van Vliet, A., and Woeginger, G. A lower bound for randomized on-line scheduling algorithms. Information Processing Letters 51, 5 (September 1994), 219–22.
Chen, B., van Vliet, A., and Woeginger, G. New lower and upper bounds for on-line scheduling. Operations Research Letters 16, 4 (November 1994), 221–230.
Faigle, U., Kern, W., and Turàn, G. On the performance of on-line algorithms for partition problems. Acta Cybernetica 9, 2 (1989), 107–19.
Galambos, G., and Woeginger, G. An online scheduling heuristic with better worst case ratio than Graham's list scheduling. SIAM Journal on Computing 22, 2 (April 1993), 349–355.
Graham, R. Bounds for certain multiprocessing anomalies. Bell Systems Technical Journal 45 (1966), 1563–1581.
Karger, D., Phillips, S., and Torng, E. A better algorithm for an ancient scheduling problem. In Proc. 5th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (1994), pp. 132–140.
Karger, D., Phillips, S., and Torng, E. A better algorithm for an ancient scheduling problem. Journal of Algorithms 20, 2 (March 1996), 400–430.
Sgall, J.On-Line Scheduling on Parallel Machines. PhD thesis, Carnegie-Mellon University, 1994.
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© 1997 Springer-Verlag Berlin Heidelberg
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Seiden, S. (1997). Randomized algorithms for that ancient scheduling problem. In: Dehne, F., Rau-Chaplin, A., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1997. Lecture Notes in Computer Science, vol 1272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63307-3_61
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DOI: https://doi.org/10.1007/3-540-63307-3_61
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