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Some Mathematical Facts About Optimal Cache Replacement

Author:

Pierre MichaudAuthors Info & Claims

ACM Transactions on Architecture and Code Optimization (TACO), Volume 13, Issue 4

Article No.: 50, Pages 1 - 19

https://doi.org/10.1145/3017992

Published: 16 December 2016 Publication History

Abstract

This article exposes and proves some mathematical facts about optimal cache replacement that were previously unknown or not proved rigorously. An explicit formula is obtained, giving OPT hits and misses as a function of past references. Several mathematical facts are derived from this formula, including a proof that OPT miss curves are always convex, and a new algorithm called OPT tokens, for reasoning about optimal replacement.

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Cited By

Joseph DAragón JParcerisa JGonzález A(2023)Boustrophedonic Frames: Quasi-Optimal L2 Caching for Textures in GPUs2023 32nd International Conference on Parallel Architectures and Compilation Techniques (PACT)10.1109/PACT58117.2023.00019(124-136)Online publication date: 21-Oct-2023
https://doi.org/10.1109/PACT58117.2023.00019
Hasslinger GOkhovatzadeh MNtougias KHasslinger FHohlfeld O(2023)An overview of analysis methods and evaluation results for caching strategiesComputer Networks10.1016/j.comnet.2023.109583228(109583)Online publication date: Jul-2023
https://doi.org/10.1016/j.comnet.2023.109583
Ding CChen DLiu FReber BSmith W(2022)CARL: Compiler Assigned Reference LeasingACM Transactions on Architecture and Code Optimization10.1145/349873019:1(1-28)Online publication date: 17-Mar-2022
https://dl.acm.org/doi/10.1145/3498730
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Index Terms

Some Mathematical Facts About Optimal Cache Replacement
1. Computer systems organization
  1. Architectures
    1. Serial architectures
      1. Superscalar architectures
2. Theory of computation
  1. Design and analysis of algorithms
    1. Online algorithms
      1. Caching and paging algorithms

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Published In

cover image ACM Transactions on Architecture and Code Optimization

ACM Transactions on Architecture and Code Optimization Volume 13, Issue 4

December 2016

648 pages

ISSN:1544-3566

EISSN:1544-3973

DOI:10.1145/3012405

Editor:
Koen De Bosschere
Ghent University

Issue’s Table of Contents

Copyright © 2016 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 16 December 2016

Accepted: 01 November 2016

Revised: 01 November 2016

Received: 01 August 2016

Published in TACO Volume 13, Issue 4

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Cited By

Joseph DAragón JParcerisa JGonzález A(2023)Boustrophedonic Frames: Quasi-Optimal L2 Caching for Textures in GPUs2023 32nd International Conference on Parallel Architectures and Compilation Techniques (PACT)10.1109/PACT58117.2023.00019(124-136)Online publication date: 21-Oct-2023
https://doi.org/10.1109/PACT58117.2023.00019
Hasslinger GOkhovatzadeh MNtougias KHasslinger FHohlfeld O(2023)An overview of analysis methods and evaluation results for caching strategiesComputer Networks10.1016/j.comnet.2023.109583228(109583)Online publication date: Jul-2023
https://doi.org/10.1016/j.comnet.2023.109583
Ding CChen DLiu FReber BSmith W(2022)CARL: Compiler Assigned Reference LeasingACM Transactions on Architecture and Code Optimization10.1145/349873019:1(1-28)Online publication date: 17-Mar-2022
https://dl.acm.org/doi/10.1145/3498730
Song SKhan TShahri SSriraman ASoundararajan NSubramoney SJiménez DLitz HKasikci BSalapura VZahran MChong FTang L(2022)ThermometerProceedings of the 49th Annual International Symposium on Computer Architecture10.1145/3470496.3527430(742-756)Online publication date: 18-Jun-2022
https://dl.acm.org/doi/10.1145/3470496.3527430
Joseph DAragon JParcerisa JGonzalez A(2022)TCOR: A Tile Cache with Optimal Replacement2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA)10.1109/HPCA53966.2022.00055(662-675)Online publication date: May-2022
https://doi.org/10.1109/HPCA53966.2022.00055
Banditwattanawong TMasdisornchote M(2021)On formulation of online algorithm and framework of near-optimally tractable eviction for nonuniform cachesComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2020.107332178:COnline publication date: 23-Aug-2021
https://dl.acm.org/doi/10.1016/j.comnet.2020.107332
Zhang LKarimi RAhmad IVigfusson Y(2020)Optimal Data Placement for Heterogeneous Cache, Memory, and Storage SystemsProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/33794724:1(1-27)Online publication date: 5-Jun-2020
https://dl.acm.org/doi/10.1145/3379472
Ben Hassine NMinet PMarinca DBarth D(2019)Popularity prediction–based caching in content delivery networksAnnals of Telecommunications10.1007/s12243-018-00700-874:5-6(351-364)Online publication date: 15-Feb-2019
https://doi.org/10.1007/s12243-018-00700-8
Banditwattanawong T(2018)The Optimality and Complexity of Offline Cache Replacement Policies for Nonuniform ObjectsInternational Journal of Future Computer and Communication10.18178/ijfcc.2018.7.3.5227:3(63-67)Online publication date: Oct-2018
https://doi.org/10.18178/ijfcc.2018.7.3.522
Berger DBeckmann NHarchol-Balter M(2018)Practical Bounds on Optimal Caching with Variable Object SizesProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/32244272:2(1-38)Online publication date: 13-Jun-2018
https://dl.acm.org/doi/10.1145/3224427
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