## The K-Server Dual and Loose Competitiveness for Paging (1994)

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Venue: | Algorithmica |

Citations: | 61 - 6 self |

### BibTeX

@ARTICLE{Young94thek-server,

author = {Neal Young},

title = {The K-Server Dual and Loose Competitiveness for Paging},

journal = {Algorithmica},

year = {1994},

volume = {11},

pages = {525--541}

}

### Years of Citing Articles

### OpenURL

### Abstract

Weighted caching is a generalization of paging in which the cost to

### Citations

1283 |
Combinatorial Optimization: Algorithms and Complexity
- Papadimitriou, Steiglitz
- 1982
(Show Context)
Citation Context ...obtained by ignoring the H[\Delta] values and lowering as little as possible in the Relabel step. 3 We will assume familiarity with linear programming primal-dual techniques. For an introduction, see =-=[PS82]-=-. 3 GreedyDual Maintain a pair of real values L[s]sH[s] with each server s. In response to each request, let v be the requested node; if some server s is on v then let H[s] / w(v) else if some server ... |

727 |
TARJAN, Amortized efficiency of list update and paging rules
- SLEATOR, E
- 1985
(Show Context)
Citation Context ...ms. We generalize them both, obtaining a single k k\Gammah+1 - competitive, primal-dual strategy for weighted caching. We introduce loose competitiveness, motivated by Sleator and Tarjan 's complaint =-=[ST85]-=- that the standard competitive ratios for paging strategies are too high. A k-server strategy is loosely c(k)-competitive if, for any sequence, for almost all k, the cost incurred by the strategy with... |

350 | A general approximation technique for constrained forest problems
- Goemans, Williamson
- 1995
(Show Context)
Citation Context ...n. The primal-dual approach has been used extensively for exact optimization problems [PS82], and is used implicitly in a number of recent analyses of approximation algorithms. Goemans and Williamson =-=[GW92]-=- explicitly use the approach for finding approximate solutions to NP-hard connectivity problems. 1.2 A more realistic k-server model In x3 we give the second contribution of this paper: loose competit... |

185 | An optimal on-line algorithm for metrical task system
- Borodin, Linial, et al.
- 1992
(Show Context)
Citation Context ...sponse to any request, any server that has not yet served a request may be placed on the requested node at no cost. Following a number of authors (Sleator and Tarjan [ST85]; Borodin, Linial, and Saks =-=[BLS87]-=-; and Manasse, McGeoch, and Sleator [MMS90]), we are interested in strategies that are competitive, that is, strategies that on any sequence incur a cost bounded by some constant times the minimum cos... |

164 | Competitive paging algorithms - Fiat, Karp, et al. - 1991 |

138 | On the power of randomization in online algorithms - Ben-David, Karp, et al. - 1990 |

138 |
Competitive algorithms for server problem
- Manasse, McGeoch, et al.
- 1990
(Show Context)
Citation Context ...ractical on-line problems, including linear search, paging, font caching, and motion planning for two-headed disks. We focus on two special cases of the k-server problem: the weighted caching problem =-=[MMS90]-=-, in which d(u; v) = w(u) for u 6= v (the cost to move a server from a node depends only on the node), and the paging problem [ST85], in which the cost to move a server is uniformly 1. Traditionally, ... |

120 | Competitive Paging with Locality of Reference
- Borodin, Irani, et al.
- 1995
(Show Context)
Citation Context ...k !1 and both c(k) and 2 ln k \Gamma c(k) are non-decreasing. Loose competitive ratios are thus shown to be exponentially lower than standard competitive ratios. Borodin, Irani, Raghavan and Scheiber =-=[BIRS91]-=- give a related work, in which the possible request sequences are quantified by the degree to which they exhibit a certain kind of locality of reference, and competitive ratios are considered as a fun... |

112 |
A strongly competitive randomized paging algorithm
- McGeoch, Sleator
- 1991
(Show Context)
Citation Context ...88, You91a] introduce and analyze Mark, showing that it is 2H k -competitive (H ksln k), and showing that no randomized paging strategy is better than H k -competitive when h = k. McGeoch and Sleator =-=[MS89]-=- subsequently give a H k -competitive randomized paging strategy. Young [You91b] shows that Mark is roughly 2 ln k k\Gammah -competitive when h ! k and that no randomized strategy is better than rough... |

73 | New results on server problems
- Chrobak, Karloff, et al.
- 1991
(Show Context)
Citation Context ...timal costs. The primal-dual approach also has the potential to unify the arguably ad hoc existing on-line analyses. For instance, the analyses of Lru and Fifo [ST85], of Balance for weighted caching =-=[CKPV91]-=-, and of Mark [FKL + 88] can all be cast as closely related primal-dual analyses. The primal-dual approach can also reveal connections to existing optimization theory. For these reasons, we take pains... |

73 | Strongly competitive algorithms for paging with locality of reference
- Irani, Karlin, et al.
- 1996
(Show Context)
Citation Context ...by the degree to which they exhibit a certain kind of locality of reference, and competitive ratios are considered as a function of this parameter. The work is extended by Irani, Karlin, and Phillips =-=[IKP92]-=-. The ratios shown in their model are, in most cases, much higher than the loose competitive ratios established in this paper. 2 GreedyDual In this section we develop and analyse GreedyDual. We first ... |

45 |
On-line caching as cache size varies
- Young
- 1991
(Show Context)
Citation Context ...H ksln k), and showing that no randomized paging strategy is better than H k -competitive when h = k. McGeoch and Sleator [MS89] subsequently give a H k -competitive randomized paging strategy. Young =-=[You91b]-=- shows that Mark is roughly 2 ln k k\Gammah -competitive when h ! k and that no randomized strategy is better than roughly ln k k\Gammah - competitive. Manasse, McGeoch, and Sleator [MMS90] show that ... |

27 |
MultÃ¾rocessor Cache Analysis Using ATUM
- Sites, Agarwal
- 1988
(Show Context)
Citation Context ...ing fraction of the values of k in any range f1; :::; ng, either X is c(k)- competitive in the usual sense, or the cost to X with k servers is insignificant 4 The input sequence, traced by Dick Sites =-=[SA88], consists-=- of 692,057 requests to 642 distinct pages of 1024 bytes each. The sequence was generated by two X-windows network processes, a "make" (program compilation), and a disk copy running concurre... |

20 |
An optimal on-line algorithm for k-servers on trees
- Chrobak, Larmore
- 1991
(Show Context)
Citation Context ...; v). A strategy for solving the problem is on-line if it chooses the server to move independently of later requests. The goal is to minimize the total cost. As many authors (e.g. Chrobak and Larmore =-=[CL91]-=-) have pointed out, the k-server problem is an abstraction of a number of practical on-line problems, including linear search, paging, font caching, and motion planning for two-headed disks. We focus ... |

18 |
Sundar Vishwanathan. New results on server problems
- Chrobak, Karloff, et al.
- 1991
(Show Context)
Citation Context ...timal costs. The primal-dual approach also has the potential to unify the arguably ad hoc existing on-line analyses. For instance, the analyses of Lru and Fifo [ST85], of Balance for weighted caching =-=[CKPV91]-=-, and of Mark [FKL + 91] can all be cast as closely related primal-dual analyses. The primal-dual approach can also reveal connections to existing optimization theory. For these reasons, we take pains... |

8 |
Competitive paging and dual-guided algorithms for weighted caching and matching
- Young
- 1991
(Show Context)
Citation Context ... at most k times during any consecutive subsequence requesting k or fewer distinct items. Lru, Fifo, Mark, and even Fwf are conservative. Any conservative paging strategy is k k\Gammah+1 -competitive =-=[You91a]-=-. The results we obtain are as follows: any conservative paging strategy is loosely c(k)-competitive provided c(k)= ln k ! 1 and both c(k) 7 and k=c(k) are non-decreasing; Mark is loosely c(k)-competi... |

3 | Algorithms for Two Graph Problems - McGeoch - 1987 |