Abstract
Weighted caching is a generalization ofpaging in which the cost to evict an item depends on the item. We study both of these problems as restrictions of the well-knownk-server problem, which involves moving servers in a graph in response to requests so as to minimize the distance traveled.
We give a deterministic on-line strategy for weighted caching that, on any sequence of requests, given a cache holdingk items, incurs a cost within a factor ofk/(k−h+1) of the minimum cost possible given a cache holdingh items. The strategy generalizes “least recently used,” one of the best paging strategies in practice. The analysis is a primal-dual analysis, the first for an on-line problem, exploiting the linear programming structure of thek-server problem.
We introduceloose competitiveness, motivated by Sleator and Tarjan's complaint [ST] that the standard competitive ratios for paging strategies are too high. Ak-server strategy isloosely c(k)-competitive if, for any sequence, foralmost all k, the cost incurred by the strategy withk serverseither is no more thanc(k) times the minimum costor is insignificant.
We show that certain paging strategies (including “least recently used,” and “first in first out”) that arek-competitive in the standard model are looselyc(k)-competitive providedc(k)/Ink→∞ and bothk/c(k) andc(k) are nondecreasing. We show that the marking algorithm, a randomized paging strategy that is Θ(Ink)-competitive in the standard model, is looselyc(k)-competitive providedk−2 In Ink→∞ and both 2 Ink−c(k) andc(k) are nondecreasing.
Similar content being viewed by others
References
S. Ben-David, A. Borodin, R. Karp, G. Tardos, and A. Wigderson. On the power of randomization in on-line algorithms.Proc. 22nd Annual ACM Symp. on Theory of Computing, Baltimore, MD, May 1990, pages 379–386. Also inAlgorithmica,11:2–14, January 1994.
A. Borodin, S. Irani, P. Raghavan, and B. Schieber. Competitive paging with locality of reference.Proc. 23rd Annual ACM Symp. on Theory of Computing, New Orleans, LA, May 1991, pages 249–259.
A. Borodin, M. Linial, and M. Saks. An optimal online algorithm for metrical task systems.Proc. 19th Annual ACM Symp. on Theory of Computing, New York, May 1987, pages 373–382. Also to appear inJ. Assoc. Comput. Mach.
M. Chrobak, H. Karloff, T. Payne, and S. Vishwanathan. new results on server problems.SIAM J. Discrete Math.,4(2): 172–181, May 1991.
M. Chrobak and L. Larmore. An optimal on-line algorithm fork-servers on trees.SIAM J. Comput.,20(1): 144–148, February 1991.
A. Fiat, R. M. Karp, M. Luby, L. A. McGeoch, D. D. Sleator, and N. E. Young. Competitive paging algorithms, Technical Report CMU-CS-88-196, Computer Science Department, Carnegie Mellon University, 1988.J. Algorithms, to appear.
M. X. Goemans and D. P. Williamson. A general approximation technique for constrained forest problems.Proc. 3rd Annual ACM-SIAM Symp. on Discrete Algorithms, Orlando, FL, January 1992, pages 317–324.
S. Irani, A. R. Karlin, and S. Phillips. Strongly competitive algorithms for paging with locality of reference.Proc. 3rd Annual ACM-SIAM Symp. on Discrete Algorithms, Orlando, FL, January 1992, pages 228–236.
L. A. McGeoch. Algorithms for Two Graph Problems. Ph.D. Thesis, Carnegie Mellon University, 1987.
M. S. Manasse, L. A. McGeoch, and D. D. Sleator. Competitive algorithms for server problems.J. Algorithms,11:208–230, 1990.
L. A. McGeoch and D. D. Sleator. A strongly competitive randomized paging algorithm.Algorithmica,6:816–825, 1991.
C. H. Papadimitriou and K. Steiglitz.Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Englewood Cliffs, NJ, 1982.
R. L. Sites and A. Agarwal. Multiprocessor cache analysis using ATUM.Proc. 15th IEEE Internat. Symp. on Computer Architecture, Honolulu, HI, 1988, pages 186–195.
D. D. Sleator and R. E. Tarjan. Amortized efficiency of list update and paging rules.Comm. ACM,28(2):202–208, February 1985.
N. Young. Competitive paging and dual-guided algorithms for weighted caching and matching. (Thesis) Technical Report CS-TR-348-91, Computer Science Department, Princeton University, October 1991.
N. Young. On-line caching as caches size varies.Proc. 2nd Annual ACM-SIAM Symp. on Discrete Algorithms, San Francisco, CA, January 1991, pages 241–250.
Author information
Authors and Affiliations
Additional information
Communicated by Prabhakar Raghavan.
This paper is the journal version of “On-line Caching as Cache Size Varies,” which appeared in theProceedings of the 2nd Annual ACM-SIAM Symposium on Discrete Algorithms (1991). Details beyond those in this paper may be found in “Competitive Paging and Dual-Guided Algorithms for Weighted Caching and Matching,” which is the author's thesis and is available as Technical Report CS-TR-348-91 from the Computer Science Department at Princeton University.
This research was performed while the author was at the Computer Science Department, Princeton University, Princeton, NJ 08544, USA, and was supported by the Hertz Foundation.
Rights and permissions
About this article
Cite this article
Young, N. Thek-server dual and loose competitiveness for paging. Algorithmica 11, 525–541 (1994). https://doi.org/10.1007/BF01189992
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01189992