Abstract
Motivated by applications in data compression, debugging, and physical simulation, we consider the problem of adaptively choosing locations in a long computation at which to save intermediate results. Such checkpoints allow faster recomputation of arbitrary requested points within the computation. We abstract the problem to a server problem in whichk servers move along a line in a single direction, modeling the fact that most computations are not reversible. Since checkpoints may be arbitrarily copied, we allow a server to jump to any location currently occupied by another server. We present on-line algorithms and analyze their competitiveness. We give lower bounds on the competitiveness of any on-line algorithm and show that our algorithms achieve these bounds within relatively small factors.
This is a preview of subscription content, log in via an institution to check access.
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 Online Algorithms,Proc. 22th ACM Symp. on Theory of Computing, 1990, pp. 379–386.
P. Berman, H. Karloff, and G. Tardos, A Competitive Three-Server Algorithm,Proc. 1st ACM-SIAM Symp. on Discrete Algorithms, 1989, pp. 280–290.
A. Borodin, N. Linial, and M. Saks, An Optimal Online Algorithm for Metrical Task Systems,Proc. 19th ACM Symp. on Theory of Computing, 1987, pp. 373–382.
A. Calderbank, E. Coffman, and L. Flatto, Sequencing Problems in Two-Server Systems,Math. Oper. Res. 10 (1985), 585–595.
M. Chrobak, H. Karloff, T. Payne, and S. Vishwanathan, New Results on Server Problems,SIAM J. Discrete Math. 4 (1991), 172–181.
M. Chrobak and L. Larmore, An Optimal On-Line Algorithm fork Servers on Trees,SIAM J. Comput. 20 (1991), 144–148.
R. Cole and A. Raghunathan, Online Algorithms for Finger Searching,Proc. 31st IEEE Symp. on Foundations of Computer Science, 1990, pp. 480–489.
D. Coppersmith, P. Doyle, P. Raghavan, and M. Snir, Random Walks on Weighted Graphs, and Applications to On-line Algorithms,Proc. 22th ACM Symp. on Theory of Computing, 1990, pp. 369–378.
E. Fiala and D. Greene, Data Compression with Finite Windows,Comm. ACM 32 (1989), 490–505.
E. Grove, The Harmonic OnlineK-Server Algorithm Is Competitive,Proc. 23rd ACM Symp. on Theory of Computing, 1991, pp. 260–266.
A. Karlin, M. Manasse, L. Rudolph, and D. Sleator, Competitive Snoopy Caching,Algorithmica 3 (1988), 79–119.
R. Korf, Complexity of Reverse Execution, Manuscript, 1981.
M. Manasse, L. McGeoch, and D. Sleator, Competitive Algorithms for On-line Problems,J. Algorithms 11 (1990), 208–230.
F. P. Preparata and M. I. Shamos,Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.
P. Raghavan and M. Snir, Memory vs. Randomization in Online Algorithms,Proc. 16th Internat. Colloq. on Automata, Languages, and Programming, Lecture Notes in Computer Science, vol. 372, Springer-Verlag, Berlin, 1989, pp. 687–703.
D. Sleator and R. Tarjan, Amortized Efficiency of List Update and Paging Rules,Comm. ACM 28 (1985), 202–208.
J. Storer,Data Compression, Computer Science Press, Rockville, MD, 1988.
Author information
Authors and Affiliations
Additional information
Communicated by Prabhakar Raghavan.
This work was done partly while at Courant Institute, New York University, NY 10012, USA.
This research was supported in part by NSF Grant CCR-8947792.
Rights and permissions
About this article
Cite this article
Bern, M., Greene, D.H., Raghunathan, A. et al. On-line algorithms for locating checkpoints. Algorithmica 11, 33–52 (1994). https://doi.org/10.1007/BF01294262
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01294262