Abstract
We consider randomized algorithms for on-line scheduling on identical machines. For two machines, a randomized algorithm achieving a competitive ratio of \(\tfrac{4}{3}\) was found by Bartal et al. (1995). Seiden has presented a randomized algorithm which achieves competitive ratios of 1.55665, 1.65888, 1.73376, 1.78295, and 1.81681, for m=3, 4, 5, 6, 7, respectively (Seiden, 2000). A barely random algorithm is one which is a distribution over a constant number of deterministic strategies. The algorithms of Bartal et al. and Seiden are not barely random–in fact, these algorithms potentially make a random choice for each job scheduled. We present the first barely random on-line scheduling algorithms. In addition, our algorithms use less space and time than the previous algorithms, asymptotically.
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Seiden, S. Barely Random Algorithms for Multiprocessor Scheduling. Journal of Scheduling 6, 309–334 (2003). https://doi.org/10.1023/A:1022960526107
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DOI: https://doi.org/10.1023/A:1022960526107