Abstract
We consider the list-update problem introduced by Sleator and Tarjan, specializing it to the case of accesses only and focusing on short lists. We describe a new optimal offline algorithm, faster than the best previous algorithm when the number of accesses is sufficiently large relative to the number ℓ of items. We also give a simple optimal offline algorithm for ℓ= 3. Taking c ℓ to denote the best competitive ratio of a randomized online algorithm for the list-access problem with ℓ items, we demonstrate that c 3 = 6/5 and give new upper and lower bounds on c 4. Finally we prove a strengthened lower bound for general ℓ.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Albers, S., von Stengel, B., Werchner, R.: A combined BIT and TIMESTAMP algorithm for the list update problem. Inform. Process. Lett. 56, 135–139 (1995)
Albers, S., von Stengel, B., Werchner, R.: List update posets, Manuscript (1996)
Bentley, J.L., McGeoch, C.C.: Amortized analyses of self-organizing sequential search heuristics. Comm. Assoc. Comput. Mach. 28, 404–411 (1985)
Chrobak, M., Larmore, L.L.: The server problem and on-line games. DIMACS Series in Disc. Math. and Theoret. Comput. Sci. 7, 11–64 (1992)
Irani, S.: Two results on the list update problem. Inform. Process. Lett. 38, 301–306 (1991)
Reingold, N., Westbrook, J.: Off-line algorithms for the list update problem. Inform. Process. Lett. 60, 75–80 (1996)
Reingold, N., Westbrook, J., Sleator, D.D.: Randomized competitive algorithms for the list update problem. Algorithmica 11, 15–32 (1994)
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Comm. Assoc. Comput. Mach. 28, 202–208 (1985)
Teia, B.: A lower bound for randomized list update algorithms. Inform. Process. Lett. 47, 5–9 (1993)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hagerup, T. (2007). Online and Offline Access to Short Lists. In: Kučera, L., Kučera, A. (eds) Mathematical Foundations of Computer Science 2007. MFCS 2007. Lecture Notes in Computer Science, vol 4708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74456-6_61
Download citation
DOI: https://doi.org/10.1007/978-3-540-74456-6_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74455-9
Online ISBN: 978-3-540-74456-6
eBook Packages: Computer ScienceComputer Science (R0)