A new upper bound on the work function algorithm for the k-server problem

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 ACM 42(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 \(2k-1\).