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The k -server problem is a generalization of the paging problems, and is the most studied problem in the area of competive online problems. The Harmonic algorithm is a very natural and simple randomized algorithm for the k -server problem. We give a simple proof that the Harmonic k -server algorithm is competitive. The competitive ratio we prove is the best currently known fo the algorithm. The Harmonic algorithm is memoryless and time-efficient. This is the only such algorithm known to be competitive for the k -server problem.
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Bartal et al. (2000) studied this question.
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