On-line 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.

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