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An O(log k)-competitive algorithm for generalized caching

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Adamaszek, Anna, Czumaj, Artur, Englert, Matthias and Räcke , Harald (2018) An O(log k)-competitive algorithm for generalized caching. ACM Transactions on Algorithms , 15 (1). pp. 1-18. 6. doi:10.1145/3280826

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Official URL: https://doi.org/10.1145/3280826

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Abstract

In the generalized caching problem, we have a set of pages and a cache of size k. Each page p has a size wpe1 and fetching cost cp for loading the page into the cache. At any point in time, the sum of the sizes of the pages stored in the cache cannot exceed k. The input consists of a sequence of page requests. If a page is not present in the cache at the time it is requested, it has to be loaded into the cache incurring a cost of cp. We give a randomized O(log k)-competitive online algorithm for the generalized caching problem, improving the previous bound of O(log2 k) by Bansal, Buchbinder, and Naor (STOC'08). This improved bound is tight and of the same order as the known bounds for the classic problem with uniform weights and sizes. We use the same LP based techniques as Bansal et al. but provide improved and slightly simplified methods for rounding fractional solutions online.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH): Cache memory, Online algorithms
Journal or Publication Title: ACM Transactions on Algorithms
Publisher: Association for Computing Machinery, Inc.
ISSN: 1549-6325
Official Date: 30 November 2018
Dates:
DateEvent
30 November 2018Available
5 September 2018Accepted
Volume: 15
Number: 1
Page Range: pp. 1-18
Article Number: 6
DOI: 10.1145/3280826
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: © Adamaszek, Anna, Czumaj, Artur, Englert, Matthias and Räcke , Harald (2018) ACM. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in ACM Transactions on Algorithms, http://dx.doi.org/10.1145/3280826
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/D063191/1 [EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/F043333/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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