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Abstract

In the online checkpointing problem, the task is to continuously maintain a
set of k checkpoints that allow to rewind an ongoing computation faster than
by a full restart. The only operation allowed is to replace an old checkpoint
by the current state. Our aim are checkpoint placement strategies that minimize
rewinding cost, i.e., such that at all times T when requested to rewind to
some time t ≤ T the number of computation steps that need to be redone to
get to t from a checkpoint before t is as small as possible. In particular,
we want that the closest checkpoint earlier than t is not further away from
t than q_k times the ideal distance T / (k+1), where q_k is a small
constant.

Improving over earlier work showing 1 + 1/k ≤ q_k ≤ 2, we show that
q_k can be chosen asymptotically less than 2. We present algorithms with
asymptotic discrepancy q_k ≤ 1.59 + o(1) valid for all k and q_k ≤
\ln(4) + o(1) ≤ 1.39 + o(1) valid for k being a power of two. Experiments
indicate the uniform bound p_k ≤ 1.7 for all k. For small k, we show
how to use a linear programming approach to compute good checkpointing
algorithms. This gives discrepancies of less than 1.55 for all k < 60.

We prove the first lower bound that is asymptotically more than one, namely
q_k ≥ 1.30 - o(1). We also show that optimal algorithms (yielding the
infimum discrepancy) exist for all~k.