Pierre Michaud
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.
- A. V. Aho, P. J. Denning, and J. D. Ullman. 1971. Principles of optimal page replacement. Journal of the ACM 18, 1 (Jan. 1971). Google Scholar
Digital Library
- N. Beckmann and D. Sanchez. 2015. Talus: A simple way to remove cliffs in cache performance. In International Symposium on High Performance Computer Architecture (HPCA).Google Scholar
- L. A. Belady. 1966. A study of replacement algorithms for virtual-storage computers. IBM Systems Journal 5, 2 (1966). Google ScholarDigital Library
- L. A. Belady and F. P. Palermo. 1974. On-line measurement of paging behavior by the multivalued MIN algorithm. IBM Journal of Research and Development 18, 1 (Jan. 1974). Google ScholarDigital Library
- J. Brock, X. Gu, B. Bao, and C. Ding. 2013. Pacman: Program-assisted cache management. In International Symposium on Memory Management (ISMM). Google ScholarDigital Library
- D. Burger and T. M. Austin. 1997. The simplescalar tool set, version 2.0. ACM SIGARCH Computer Architecture News 25, 3 (June 1997). Google ScholarDigital Library
- E. G. Coffman and P. J. Denning. 1973. Operating Systems Theory. Prentice-Hall. Google ScholarDigital Library
- A. Cohen and W. A. Burkhard. 1995. A proof of the optimality of the MIN paging algorithm using linear programming duality. Operations Research Letters 18, 1 (Aug. 1995). Google ScholarDigital Library
- A. Jain and C. Lin. 2016. Back to the future: Leveraging Belady’s algorithm for improved cache replacement. In International Symposium on Computer Architecture (ISCA). Google ScholarDigital Library
- D. E. Knuth. 1985. An analysis of optimum caching. Journal of Algorithms 6, 2 (June 1985). Google ScholarDigital Library
- M.-K. Lee, P. Michaud, J. S. Sim, and D. Nyang. 2016. A simple proof of optimality for the MIN cache replacement policy. Information Processing. Letters 116, 2 (Feb. 2016). Google ScholarDigital Library
- W.-F. Lin and S. Reinhardt. 2002. Predicting Last-Touch References Under Optimal Replacement. Technical Report CSE-TR-447-02. University of Michigan.Google Scholar
- R. L. Mattson, J. Gecsei, D. R. Slutz, and I. L. Traiger. 1970. Evaluation techniques for storage hierarchies. IBM Systems Journal 9, 2 (1970). Google ScholarDigital Library
- S. McFarling. 1991. Program Analysis And Optimization For Machines With Instruction Cache. Ph.D. dissertation. Stanford University. Google ScholarDigital Library
- T. R. Puzak. 1985. Analysis of Cache Replacement Algorithms. Ph.D. dissertation. University of Massachusetts Amherst. Google ScholarDigital Library
- K. Rajan and R. Govindarajan. 2007. Emulating optimal replacement with a shepherd cache. In International Symposium on Microarchitecture (MICRO). Google ScholarDigital Library
- A. J. Smith. 1976. Analysis of the optimal, look-ahead demand paging algorithms. SIAM Journal on Computing 5, 4 (Dec. 1976).Google ScholarCross Ref
- J. E. Smith and J. R. Goodman. 1985. Instruction cache replacement policies and organizations. IEEE Transactions on Computers C-34, 3 (March 1985). Google ScholarDigital Library
- R. A. Sugumar and S. G. Abraham. 1993. Efficient simulation of caches under optimal replacement with applications to miss characterization. In ACM SIGMETRICS. Google ScholarDigital Library
- O. Temam. 1999. An algorithm for optimally exploiting spatial and temporal locality in upper memory levels. IEEE Transactions on Computers 48, 2 (Feb. 1999). Google ScholarDigital Library
- B. Van Roy. 2007. A short proof of optimality for the MIN cache replacement algorithm. Information Processing Letters 102, 2 (April 2007). Google ScholarDigital Library
- W. Vogler. 2008. Another short proof of optimality for the MIN cache replacement algorithm. Information Processing Letters 106, 5 (May 2008). Google ScholarDigital Library
Index Terms
- Some Mathematical Facts About Optimal Cache Replacement
Recommendations
High performance cache replacement using re-reference interval prediction (RRIP)
ISCA '10: Proceedings of the 37th annual international symposium on Computer architecturePractical cache replacement policies attempt to emulate optimal replacement by predicting the re-reference interval of a cache block. The commonly used LRU replacement policy always predicts a near-immediate re-reference interval on cache hits and ...
High performance cache replacement using re-reference interval prediction (RRIP)
ISCA '10Practical cache replacement policies attempt to emulate optimal replacement by predicting the re-reference interval of a cache block. The commonly used LRU replacement policy always predicts a near-immediate re-reference interval on cache hits and ...
A new cache replacement algorithm for last-level caches by exploiting tag-distance correlation of cache lines
Cache memory plays a crucial role in determining the performance of processors, especially for embedded processors where area and power are tightly constrained. It is necessary to have effective management mechanisms, such as cache replacement policies, ...
Comments