Randomized competitive algorithms for generalized caching

Nikhil Bansal*, Niv Buchbinder, Joseph Naor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

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. Our main result is an online algorithm with competitive ratio O(log 2 k), which gives the first o(k) competitive algorithm for the problem. We also give improved O(log k)-competitive algorithms for the special cases of the bit model and fault model, improving upon the previous O(log 2 k) guarantees due to Irani [Proceedings of the 29th Annual ACM Symposium on Theory of Computing, 1997, pp. 701- 710]. Our algorithms are based on an extension of the online primal-dual framework introduced by Buchbinder and Naor [Math. Oper. Res., 34 (2009), pp. 270-286] and involve two steps. First, we obtain an O(log k)-competitive fractional algorithm based on solving online an LP formulation strengthened with exponentially many knapsack cover constraints. Second, we design a suitable online rounding procedure to convert this online fractional algorithm into a randomized algorithm. Our techniques provide a unified framework for caching algorithms and are substantially simpler than those previously used.

Original languageEnglish
Pages (from-to)391-414
Number of pages24
JournalSIAM Journal on Computing
Volume41
Issue number2
DOIs
StatePublished - 2012
Externally publishedYes

Keywords

  • Competitive analysis
  • Generalized caching
  • Paging
  • Randomization

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