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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© 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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