Tight Bounds for Parallel Paging and Green Paging
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Publication Date:
NSF-PAR ID:
10297262
Journal Name:
Proceedings of the annual ACMSIAM symposium on discrete algorithms
ISSN:
2160-1445
1. In the parallel paging problem, there are $\pP$ processors that share a cache of size $k$. The goal is to partition the cache among the \procs over time in order to minimize their average completion time. For this long-standing open problem, we give tight upper and lower bounds of $\Theta(\log \p)$ on the competitive ratio with $O(1)$ resource augmentation. A key idea in both our algorithms and lower bounds is to relate the problem of parallel paging to the seemingly unrelated problem of green paging. In green paging, there is an energy-optimized processor that can temporarily turn off one or more of its cache banks (thereby reducing power consumption), so that the cache size varies between a maximum size $k$ and a minimum size $k/\p$. The goal is to minimize the total energy consumed by the computation, which is proportional to the integral of the cache size over time. We show that any efficient solution to green paging can be converted into an efficient solution to parallel paging, and that any lower bound for green paging can be converted into a lower bound for parallel paging, in both cases in a black-box fashion. We then show that, with $O(1)$ resourcemore »