On the k-server conjecture

We prove that the <italic>work function algorithm</italic> for the <italic>k</italic>-server problem has a competitive ratio at most 2<italic>k</italic>−1. Manasse et al. [1988] conjectured that the competitive ratio for the <italic>k</italic>-server problem is exactly <italic>k</italic> (it is trivially at least <italic>k</italic>); previously the best-known upper bound was exponential in <italic>k</italic>. Our proof involves three crucial ingredients: A <italic>quasiconvexity property</italic> of work functions, a <italic>duality lemma</italic> that uses quasiconvexity to characterize the configuration that achieve maximum increase of the work function, and a <italic>potential function</italic> that exploits the duality lemma.

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