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Efficient stack distance computation for priority replacement policies

Published: 03 May 2011 Publication History

Abstract

The concept of stack distance, applicable to the important class of inclusion replacement policies for the memory hierarchy, enables to efficiently compute the number of misses incurred on a given address trace, for all cache sizes. The concept was introduced by Mattson, Gecsei, Sluts, and Traiger (Evaluation techniques for storage hierarchies, IBM System Journal, (9)2:78-117, 1970), together with a Linear-Scan algorithm, which takes time O(V) per access, in the worst case, where V is the number of distinct (virtual) items referenced within the trace. While subsequent work has lowered the time bound to O(log V) per access in the special case of the Least Recently Used policy, no improvements have been obtained for the general case.
This work introduces a class of inclusion policies called policies with nearly static priorities, which encompasses several of the policies considered in the literature. The Min-Tree algorithm is proposed for these policies. The performance of the Min-Tree algorithm is very sensitive to the replacement policy as well as to the address trace. Under suitable probabilistic assumptions, the expected time per access is O(log2 V). Experimental evidence collected on a mix of benchmarks shows that the Min-Tree algorithm is significantly faster than Linear-Scan, for interesting policies such as OPT (or Belady), Least Frequently Used (LFU), and Most Recently Used (MRU). As a further advantage, Min-Tree can be parallelized to run in time O(log V) using O(V/log V) processors, in the worst case.
A more sophisticated Lazy Min-Tree algorithm is also developed which achieves O(√ log V) worst-case time per access. This bound applies, in particular, to the policies OPT, LFU, and Least Recently/Frequently Used (LRFU), for which the best previously known bound was O(V).

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Cited By

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  • (2023)Increment - and - Freeze: Every Cache, Everywhere, All of the TimeProceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3558481.3591085(129-139)Online publication date: 17-Jun-2023
  • (2023)Multi-Tenant In-Memory Key-Value Cache Partitioning Using Efficient Random Sampling-Based LRU ModelIEEE Transactions on Cloud Computing10.1109/TCC.2023.330088911:4(3601-3618)Online publication date: Oct-2023
  • (2021)Efficient Modeling of Random Sampling-Based LRUProceedings of the 50th International Conference on Parallel Processing10.1145/3472456.3472514(1-11)Online publication date: 9-Aug-2021
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cover image ACM Conferences
CF '11: Proceedings of the 8th ACM International Conference on Computing Frontiers
May 2011
268 pages
ISBN:9781450306980
DOI:10.1145/2016604
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 03 May 2011

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  1. optimal page replacement

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CF'11: Computing Frontiers Conference
May 3 - 5, 2011
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Cited By

View all
  • (2023)Increment - and - Freeze: Every Cache, Everywhere, All of the TimeProceedings of the 35th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3558481.3591085(129-139)Online publication date: 17-Jun-2023
  • (2023)Multi-Tenant In-Memory Key-Value Cache Partitioning Using Efficient Random Sampling-Based LRU ModelIEEE Transactions on Cloud Computing10.1109/TCC.2023.330088911:4(3601-3618)Online publication date: Oct-2023
  • (2021)Efficient Modeling of Random Sampling-Based LRUProceedings of the 50th International Conference on Parallel Processing10.1145/3472456.3472514(1-11)Online publication date: 9-Aug-2021
  • (2018)Replacement Policy Adaptable Miss Curve Estimation for Efficient Cache PartitioningIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2017.271266637:2(445-457)Online publication date: 1-Feb-2018
  • (2015)CentaurProceedings of the 2015 IEEE International Conference on Autonomic Computing10.1109/ICAC.2015.44(51-60)Online publication date: 7-Jul-2015

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