We prove that the work function algorithm for the k-server problem has
a competitive ratio at most 2k - 1. Manasse et al. [1988] conjectured
that the competitive ratio for the k-server problem is exactly k (it
is trivially at least k); previously the best-known upper bound was ex
ponential in k. Our proof involves three crucial ingredients: A quasic
onvexity property of work functions, a duality lemma that uses quasico
nvexity to characterize the configuration that achieve maximum increas
e of the work function, and a potential function that exploits the dua
lity lemma.