Online algorithms for locating checkpoints

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.

[1]  Allan Borodin,et al.  An optimal online algorithm for metrical task systems , 1987, STOC.

[2]  Marek Chrobak,et al.  New results on server problems , 1991, SODA '90.

[3]  Marek Chrobak,et al.  An Optimal On-Line Algorithm for k-Servers on Trees , 1991, SIAM J. Comput..

[4]  Robert E. Tarjan,et al.  Amortized efficiency of list update and paging rules , 1985, CACM.

[5]  Richard Cole,et al.  Online algorithms for finger searching , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[6]  James A. Storer,et al.  Data Compression: Methods and Theory , 1987 .

[7]  Edward F. Grove The harmonic online K-server algorithm is competitive , 1991, STOC '91.

[8]  James A. Storer,et al.  Data Compression , 1992, Inf. Process. Manag..

[9]  Lyle A. McGeoch,et al.  Competitive Algorithms for Server Problems , 1990, J. Algorithms.

[10]  Lyle A. McGeoch,et al.  Competitive algorithms for on-line problems , 1988, STOC '88.

[11]  Gábor Tardos,et al.  A competitive 3-server algorithm , 1990, SODA '90.

[12]  A. Robert Calderbank,et al.  Sequencing Problems in Two-Server Systems , 1985, Math. Oper. Res..

[13]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[14]  Edward R. Fiala,et al.  Data compression with finite windows , 1989, CACM.

[15]  Prabhakar Raghavan,et al.  Memory Versus Randomization in On-line Algorithms (Extended Abstract) , 1989, ICALP.

[16]  Allan Borodin,et al.  On the power of randomization in online algorithms , 1990, STOC '90.

[17]  Prabhakar Raghavan,et al.  Random walks on weighted graphs, and applications to on-line algorithms , 1990, STOC '90.