skip to main content


Title: Tight Bounds for Parallel Paging and Green Paging
Award ID(s):
1733873 1725647
NSF-PAR ID:
10297262
Author(s) / Creator(s):
; ; ; ; ;
Date Published:
Journal Name:
Proceedings of the annual ACMSIAM symposium on discrete algorithms
ISSN:
2160-1445
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. In the parallel paging problem, there are p processors that share a cache of size k. The goal is to partition the cache among the processors over time in order to minimize their average completion time. For this long-standing open problem, we give tight upper and lower bounds of ⇥(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) resource augmentation, the optimal competitive ratio for deterministic online green paging is ⇥(log p), which, in turn, implies the same bounds for deterministic online parallel paging. 
    more » « less
  2. null (Ed.)
    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 $O(1)$ resource augmentation, the optimal competitive ratio for deterministic online green paging is $\Theta(\log \p)$, which, in turn, implies the same bounds for deterministic online parallel paging. 
    more » « less
  3. Abstract This paper focuses on protecting the cellular paging protocol — which balances between the quality-of-service and battery consumption of a device — against security and privacy attacks. Attacks against this protocol can have severe repercussions, for instance, allowing attacker to infer a victim’s location, leak a victim’s IMSI, and inject fabricated emergency alerts. To secure the protocol, we first identify the underlying design weaknesses enabling such attacks and then propose efficient and backward-compatible approaches to address these weaknesses. We also demonstrate the deployment feasibility of our enhanced paging protocol by implementing it on an open-source cellular protocol library and commodity hardware. Our evaluation demonstrates that the enhanced protocol can thwart attacks without incurring substantial overhead. 
    more » « less
  4. In this article, we initiate the study of the weighted paging problem with predictions. This continues the recent line of work in online algorithms with predictions, particularly that of Lykouris and Vassilvitski (ICML 2018) and Rohatgi (SODA 2020) on unweighted paging with predictions. We show that unlike unweighted paging, neither a fixed lookahead nor a knowledge of the next request for every page is sufficient information for an algorithm to overcome the existing lower bounds in weighted paging. However, a combination of the two, which we call strong per request prediction (SPRP), suffices to give a 2-competitive algorithm. We also explore the question of gracefully degrading algorithms with increasing prediction error, and give both upper and lower bounds for a set of natural measures of prediction error. 
    more » « less