## On the k-Server Conjecture (1995)

Venue: | Journal of the ACM |

Citations: | 96 - 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...

### Citations

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Citation Context ...ornia, San Diego christos@cs.ucsd.edu May 22, 1995 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... |

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Citation Context ...ses 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,... |

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Citation Context ... some general value and applicability. For example, using a similar technique but a different potential the exact kserver conjecture was proved for the special case of metric spaces with k + 2 points =-=[20, 22]-=-. 2 The Work Function Algorithm The algorithm we employ is the work function algorithm, a rather natural idea for this problem that was first made explicit in the work of Chrobak and Larmore [9] and d... |

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Citation Context ...mpetitive algorithm for any metric space [10]. The lack of significant progress towards the k-server conjecture led to the study of special cases of the problem. One of the first results in this area =-=[3]-=- was a proof that the harmonic algorithm for 3 servers is competitive (although with a terribly high competitive ratio; this result preceded the work of [14, 16]). Attacking the problem in special met... |

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Citation Context ... some general value and applicability. For example, using a similar technique but a different potential the exact kserver conjecture was proved for the special case of metric spaces with k + 2 points =-=[20, 22]-=-. 2 The Work Function Algorithm The algorithm we employ is the work function algorithm, a rather natural idea for this problem that was first made explicit in the work of Chrobak and Larmore [9] and d... |

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Citation Context ...ly resistive metric spaces (one of them is the circle). Especially for the 2-server problem, [17] and [11] gave a 10-competitive and a 4-competitive efficient deterministic algorithm respectively and =-=[8]-=- showed that the harmonic algorithm is 3-competitive. We should also mention a series [4, 18, 19] of lower bound results for the randomized version of the k-server problem against an oblivious adversa... |

3 |
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Citation Context ...em in special metric spaces led to a k-competitive algorithm for the line [6], which was extended to trees [7]. Finally, an O(k 3 ) competitive deterministic algorithm for the circle was presented in =-=[15]-=-. 3 One of the problems with the known competitive algorithms for the kserver problem is that they are not space-efficient (the algorithm proved 2k \Gamma 1-competitive in this paper is no exception).... |