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Optimal lower bounds for projective list update algorithms

Ambuehl, Christoph, Gaertner, Bernd and von Stengel, Bernhard (2013) Optimal lower bounds for projective list update algorithms. ACM Transactions on Algorithms, 9 (4). No.31. ISSN 1549-6325

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Abstract

The list update problem is a classical online problem, with an optimal competitive ratio that is still open, known to be somewhere between 1.5 and 1.6. An algorithm with competitive ratio 1.6, the smallest known to date, is COMB, a randomized combination of BIT and the TIMESTAMP algorithm TS. This and almost all other list update algorithms, like MTF, are projective in the sense that they can be defined by looking only at any pair of list items at a time. Projectivity (also known as “list factoring”) simplifies both the description of the algorithm and its analysis, and so far seems to be the only way to define a good online algorithm for lists of arbitrary length. In this article, we characterize all projective list update algorithms and show that their competitive ratio is never smaller than 1.6 in the partial cost model. Therefore, COMB is a best possible projective algorithm in this model.

Item Type: Article
Official URL: http://dl.acm.org/pub.cfm?id=J982&CFID=213939754&C...
Additional Information: © 2013 ACM, Inc.
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 03 Oct 2013 08:22
URL: http://eprints.lse.ac.uk/45819/

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