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 2 k - 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 < 2 k , this ratio is less than 2 k - 1 .