research-article

Optimal lower bounds for projective list update algorithms

Authors:

Christoph Ambühl,

Bernd Gärtner,

Bernhard von StengelAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 9, Issue 4

Article No.: 31, Pages 1 - 18

https://doi.org/10.1145/2500120

Published: 03 October 2013 Publication History

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.

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Cited By

Angelopoulos SDorrigiv RLópez-Ortiz A(2019)On the Separation and Equivalence of Paging Strategies and Other Online AlgorithmsAlgorithmica10.1007/s00453-018-0461-281:3(1152-1179)Online publication date: 1-Mar-2019
https://dl.acm.org/doi/10.1007/s00453-018-0461-2
Ambühl C(2017)SIGACT News Online Algorithms Column 31ACM SIGACT News10.1145/3138860.313887148:3(68-82)Online publication date: 7-Sep-2017
https://dl.acm.org/doi/10.1145/3138860.3138871
Boyar JKamali SLarsen KLpez-Ortiz A(2017)On the list update problem with adviceInformation and Computation10.1016/j.ic.2016.06.007253:P3(411-423)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1016/j.ic.2016.06.007
Show More Cited By

Index Terms

Optimal lower bounds for projective list update algorithms
1. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 9, Issue 4

September 2013

131 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/2533288

Issue’s Table of Contents

Copyright © 2013 ACM.

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Association for Computing Machinery

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Publication History

Published: 03 October 2013

Accepted: 01 January 2013

Revised: 01 March 2012

Received: 01 March 2010

Published in TALG Volume 9, Issue 4

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Cited By

Angelopoulos SDorrigiv RLópez-Ortiz A(2019)On the Separation and Equivalence of Paging Strategies and Other Online AlgorithmsAlgorithmica10.1007/s00453-018-0461-281:3(1152-1179)Online publication date: 1-Mar-2019
https://dl.acm.org/doi/10.1007/s00453-018-0461-2
Ambühl C(2017)SIGACT News Online Algorithms Column 31ACM SIGACT News10.1145/3138860.313887148:3(68-82)Online publication date: 7-Sep-2017
https://dl.acm.org/doi/10.1145/3138860.3138871
Boyar JKamali SLarsen KLpez-Ortiz A(2017)On the list update problem with adviceInformation and Computation10.1016/j.ic.2016.06.007253:P3(411-423)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1016/j.ic.2016.06.007
Kamali S(2016)Online List UpdateEncyclopedia of Algorithms10.1007/978-1-4939-2864-4_266(1448-1451)Online publication date: 22-Apr-2016
https://doi.org/10.1007/978-1-4939-2864-4_266
Kamali S(2015)Online List UpdateEncyclopedia of Algorithms10.1007/978-3-642-27848-8_266-2(1-5)Online publication date: 31-Jan-2015
https://doi.org/10.1007/978-3-642-27848-8_266-2

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