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.

References

[1]

Albers, S. 1998. Improved randomized on-line algorithms for the list update problem. SIAM J. Comput. 27, 3, 682--693.

Digital Library

[2]

Albers, S., von Stengel, B., and Werchner, R. 1995. A combined BIT and TIMESTAMP algorithm for the list update problem. Inform. Process. Lett. 56, 3, 135--139.

Digital Library

[3]

Albers, S., von Stengel, B., and Werchner, R. 1996. List update posets. Manuscript. http://www.maths.lse.ac.uk/Personal/stengel/TEXTE/listupdateposets.pdf.

[4]

Albers, S. and Westbrook, J. 1998. Self-organizing data structures. In Online Algorithms, A. Fiat and G. J. Woeginger (Eds.), Lecture Notes in Computer Science, vol. 1442, Springer, 13--51.

Digital Library

[5]

Ambühl, C. 2002. On the list update problem. Ph.D. dissertation. ETH Zürich.

[6]

Ambühl, C., Gärtner, B., and von Stengel, B. 2000. Optimal projective algorithms for the list update problem. In Proceedings of the 27th International Colloquium on Automata, Languages and Programming (ICALP). 305--316.

Digital Library

[7]

Ambühl, C., Gärtner, B., and von Stengel, B. 2001. A new lower bound for the list update problem in the partial cost model. Theoret. Comput. Sci. 268, 1, 3--16.

Digital Library

[8]

Bentley, J. L. and McGeoch, C. C. 1985. Amortized analyses of self-organizing sequential search heuristics. Comm. ACM 28, 4, 404--411.

Digital Library

[9]

Borodin, A. and El-Yaniv, R. 1998. Online Computation and Competitive Analysis. Cambridge University Press, New York.

Digital Library

[10]

Dorrigiv, R., Ehmsen, M. R., and López-Ortiz, A. 2010. Parameterized analysis of paging and list update algorithms. In Proceedings of the WAOA 2009. E. Bampis and K. Jansen (Eds.), Lecture Notes in Computer Science, vol. 5893, Springer, 104--115.

Digital Library

[11]

Ehmsen, M. R., Kohrt, J. S., and Larsen, K. S. 2011. List factoring and relative worst order analysis. In Proceedings of the WAOA 2010. K. Jansen and R. Solis-Oba (Eds.), Lecture Notes in Computer Science, vol. 6534, Springer, 118--129.

Digital Library

[12]

Hagerup, T. 2007. Online and offline access to short lists. In Proceedings of the MFCS. L. Kucera and A. Kucera (Eds.), Lecture Notes in Computer Science, vol. 4708, Springer, 691--702.

Digital Library

[13]

Irani, S. 1991. Two results on the list update problem. Info. Proc. Lett. 38, 6, 301--306. (Corrected version appeared as Technical Report 96-53, ICS Department, UC Irvine, CA, USA 1996.)

Digital Library

[14]

Reingold, N., Westbrook, J., and Sleator, D. D. 1994. Randomized competitive algorithms for the list update problem. Algorithmica 11, 1, 15--32.

Digital Library

[15]

Sleator, D. D. and Tarjan, R. E. 1985. Amortized efficiency of list update and paging rules. Comm. ACM 28, 2, 202--208.

Digital Library

[16]

Teia, B. 1993. A lower bound for randomized list update algorithms. Inf. Proc. Lett. 47, 1, 5--9.

Digital Library

[17]

Yao, A. C.-C. 1977. Probabilistic computations: Toward a unified measure of complexity. In Proceedings of the 18th Annual Symposium on Foundations of Computer Science (FOCS). 222--227.

Digital Library

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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