## Page replacement with multi-size pages and applications to Web caching (1997)

Venue: | in 29th ACM STOC |

Citations: | 16 - 0 self |

### BibTeX

@INPROCEEDINGS{Irani97pagereplacement,

author = {Sandy Irani},

title = {Page replacement with multi-size pages and applications to Web caching},

booktitle = {in 29th ACM STOC},

year = {1997},

pages = {701--710}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider the paging problem where the pages have varying size. This problem has applications to page replacement policies for caches containing World Wide Web documents. We consider two models for the cost of an algorithm on a request sequence. In the rst, (the Fault model) the goal is to minimize the number of page faults. In the second, (the Bit model) the goal is to minimize the total numberofbitsthathave tobereadinto the cache. We show o ine algorithms for both cost models that obtain approximation factors of O(log k), where k is the ratio of the size of the cache to the size of the smallest page. We show randomized online algorithms for both cost models that are O(log 2 k)-competitive. In addition, if the input sequence is generated by aknown distribution, we show an algorithm for the Fault model whose expected cost is within a factor of O(log k) ofany other online algorithm. 1

### Citations

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Citation Context ... depend heavily on the o ine approximation algorithm presented in Section 4. When the pages all have the same size, there is a simple rule, due to Belady, for obtaining the optimal replacement policy =-=[Bel66]-=-: on a fault evict the page whose next request is farthest in the future. Such a simple rule for the multi-size case does not seem to exist. In fact the problem of devising the optimal replacement pol... |

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(Show Context)
Citation Context ...lti-size pages. Since these results were obtained, there have beenseveral papers that address paging with multi-size pages where the cost of bringing a page into the cache is arbitrary. Cao and Irani =-=[CI97]-=- and Young [Young98] analyze a generalization of an algorithm called greedy-dual developed by Young [Young94]. This deterministic algorithm is shown to be (k + 1)-competitive. Young shows that it is i... |

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Citation Context ...12) Evict q. (13) c(j) c(j) ;jqj. Figure 2: O ine Approximation Algorithm for the Bit Model. The analysis makes use of a potential function. (For an introduction to the use of potential functions see =-=[T85]-=-). Before de ning the potential function, some preliminary de nitions will be necessary. De ne SOBMA(l� t) to be the set of pages in class l that OBMA currently has in the cache whose next request occ... |

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Citation Context ...linear programming formulation to give an o ine algorithm that gives an approximate solution when the size of the largest page is small with respect to the size of the cache. Albers, Arora and Khanna =-=[AAK99]-=- examine the general cost model and obtain an O(1)approximation algorithm for the o ine problem that uses an additional amount of memory that is O(1) times the size of the largest page. When no additi... |

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Citation Context ... such ascheme are beyond the scope of this paper. The best competitive ratio that can be achieved byany deterministic online algorithm is achieved by the familiar Least-Recently-Used (LRU): Theorem 1 =-=[FKIP96]-=- LRUis(k+1)-competitive for the Multi-Size Optional Paging Problem in both the Fault and the Bit models. This bound is the best achievable by a deterministic online algorithm in both cost models. Thro... |

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Citation Context ... future. Such a simple rule for the multi-size case does not seem to exist. In fact the problem of devising the optimal replacement policy for a given sequence of requests is NP-hard in the Bit model =-=[Fiat97]-=-. It is unknown whether the problem is in P for the Fault model. We develop a approximation algorithms for the Fault and Bit model and prove the following theorem: Theorem 2 There isapolynomial-time o... |

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Citation Context ...orithms in Section 4 with a known algorithm for the uniform size case. We use the algorithm of Lund, Phillips and Reingold for paging when the sequence is generated by an arbitrary known distribution =-=[LPR94]-=-. The cost of the Lund et al. algorithm is within a factor of 4 of any online algorithm that knows the distribution in advance. We prove the following theorem: Theorem 4 Given a distribution over inpu... |

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Citation Context ...multi-size pages where the cost of bringing a page into the cache is arbitrary. Cao and Irani [CI97] and Young [Young98] analyze a generalization of an algorithm called greedy-dual developed by Young =-=[Young94]-=-. This deterministic algorithm is shown to be (k + 1)-competitive. Young shows that it is in fact (k +1=k ; h + 1)-competitive when the optimal algorithm has a cache size of h. Cao and Irani also perf... |

12 |
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Citation Context ...by the user. A cache can be maintained at a Web client (e.g., caches built into Web browsers) [BCC + 95] or by a Web server [KMR95]. Caches can also be very e ective when placed in the network itself =-=[DHS93]-=-. There are several possible measurements that can be used to study the e ectiveness of a caching policy. One may wish to minimize the number of requests reaching popular servers. Viewed another way, ... |

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Citation Context ...ince these results were obtained, there have beenseveral papers that address paging with multi-size pages where the cost of bringing a page into the cache is arbitrary. Cao and Irani [CI97] and Young =-=[Young98]-=- analyze a generalization of an algorithm called greedy-dual developed by Young [Young94]. This deterministic algorithm is shown to be (k + 1)-competitive. Young shows that it is in fact (k +1=k ; h +... |

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Citation Context ...uation of the algorithm using trace data. Cohen and Kaplan then give an alternate proof of the (k +1=k ; h + 1)-competitiveness of this algorithm using a linear programming formulation of the problem =-=[CK99]-=-. They use the linear programming formulation to give an o ine algorithm that gives an approximate solution when the size of the largest page is small with respect to the size of the cache. Albers, Ar... |