## On the k-Server Conjecture (1995)

Venue: | Journal of the ACM |

Citations: | 100 - 6 self |

### BibTeX

@ARTICLE{Koutsoupias95onthe,

author = {Elias Koutsoupias and Christos Papadimitriou},

title = {On the k-Server Conjecture},

journal = {Journal of the ACM},

year = {1995},

volume = {42},

pages = {507--511}

}

### Years of Citing Articles

### OpenURL

### Abstract

We prove that the work function algorithm for the k-server problem has competitive ratio at most 2k \Gamma 1. Manasse, McGeoch, and Sleator [24] 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 exponential in k. Our proof involves three crucial ingredients: A quasiconvexity property of work functions, a duality lemma that uses quasiconvexity to characterize the configurations that achieve maximum increase of the work function, and a potential function that exploits the duality lemma. 1 Introduction The k-server problem [24, 25] is defined on a metric space M, which is a (possibly infinite) set of points with a symmetric distance function d (nonnegative real function) that satisfies the triangle inequality: For all points x, y, and z d(x; x) = 0 d(x; y) = d(y; x) d(x; y) d(x; z) + d(z; y) 1 On the metric space M, k servers reside that can move from point to point. A possib...

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