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by Yossi Azar, Leah Epstein, Rob Van Stee
Algorithm Theory - SWAT 2000, 7th Scandinavian Workshop on Algorithm Theory, Proceedings, volume 1851 of Lecture Notes in Computer Science
http://www.math.tau.ac.il/~azar/extra.ps
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Abstract:
We consider load balancing in the following setting. The on-line algorithm is allowed to use n machines, whereas the optimal o-line algorithm is limited to m machines, for some xed m n. We show that while the greedy algorithm has a competitive ratio which decays linearly in the inverse of n=m, the best on-line algorithm has a ratio which decays exponentially in n=m. Specically, we give a deterministic algorithm with competitive ratio of 1 + 2 n m (1 o(1)), and a lower bound of 1 + e n m (1+o(1)) on the competitive ratio of any randomized algorithm. We also consider the preemptive case. We show an on-line algorithm with a competitive ratio of 1 + e n m (1+o(1)). We show that the algorithm is optimal by proving a matching lower bound. We also consider the non-preemptive model with temporary tasks. We prove that for n = m + 1, the greedy algorithm is optimal. (It is not optimal for permanent tasks.)
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