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Randomized competitive algorithms for generalized caching

Published: 17 May 2008 Publication History

Abstract

We consider online algorithms for the generalized caching problem. Here we are given a cache of size k and pages with arbitrary sizes and fetching costs. Given a request sequence of pages, the goal is to minimize the total cost of fetching the pages into the cache. We give an online algorithm with competitive ratio O(log2k), which is the first algorithm for the problem with competitive ratio sublinear in k. We also give improved O(log k)-competitive algorithms for the special cases of the Bit Model and Fault model. In the Bit Model, the fetching cost is proportional to the size of the page and in the Fault model all fetching costs are uniform. Previously, an O(log2 k)-competitive algorithm due to Irani [14] was known for both of these models. Our algorithms are based on an extension of the primal-dual framework for online algorithms which was developed by Buchbinder and Naor [7]. We first generate an O(log k)-competitive fractional algorithm for the problem. This is done by using a strengthened LP formulation with knapsack-cover constraints, where exponentially many constraints are added upon arrival of a new request. Second, we round online the fractional solution and obtain a randomized online algorithm. Our techniques provide a unified framework for caching algorithms and are substantially simpler than those previously used.

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    cover image ACM Conferences
    STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing
    May 2008
    712 pages
    ISBN:9781605580470
    DOI:10.1145/1374376
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    Published: 17 May 2008

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    Author Tags

    1. arbitrary sizes
    2. arbitrary weights
    3. caching
    4. knapsack cover inequalities
    5. online algorithms
    6. primal-dual analysis

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    May 17 - 20, 2008
    British Columbia, Victoria, Canada

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    STOC '08 Paper Acceptance Rate 80 of 325 submissions, 25%;
    Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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