The k-server problem was introduced by Manasse et al. (in: Proceedings of the 20th annual ACM symposium on theory of computing, Chicago, Illinois, USA, pp 322-333, 1988), and is one of the most famous and well-studied online problems. Koutsoupias and Papadimitriou (J ACM42(5):971-983, 1995) showed that the work function algorithm (WFA) has a competitive ratio of at most 2k - 1 for the k-server problem. In this paper, by proposing a potential function that is different from the one in Koutsoupias and Papadimitriou (1995), we show that the WFA has a competitive ratio of at most n - 1, where n is the number of points in the metric space. When n < 2k, this ratio is less than 2k - 1.
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