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New and Improved Bounds for Markov Paging

Authors Chirag Pabbaraju , Ali Vakilian

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Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Beyond Worst-case Analyis
  • Online Paging
  • Markov Paging

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Abstract

In the Markov paging model, one assumes that page requests are drawn from a Markov chain over the pages in memory, and the goal is to maintain a fast cache that suffers few page faults in expectation. While computing the optimal online algorithm (OPT) for this problem naively takes time exponential in the size of the cache, the best-known polynomial-time approximation algorithm is the dominating distribution algorithm due to Lund, Phillips and Reingold (FOCS 1994), who showed that the algorithm is 4-competitive against OPT. We substantially improve their analysis and show that the dominating distribution algorithm is in fact 2-competitive against OPT. We also show a lower bound of 1.5907-competitiveness for this algorithm - to the best of our knowledge, no such lower bound was previously known.

Cite As Get BibTex

Chirag Pabbaraju and Ali Vakilian. New and Improved Bounds for Markov Paging. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 123:1-123:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.123

Author Details

Chirag Pabbaraju
  • Stanford University, CA, USA
Ali Vakilian
  • Toyota Technological Institute at Chicago, IL, USA

Funding

  • Pabbaraju, Chirag: Supported by Moses Charikar and Gregory Valiant’s Simons Investigator Awards.

Acknowledgements

The authors would like to thank Avrim Blum for helpful pointers.

References

  1. Spyros Angelopoulos and Pascal Schweitzer. Paging and list update under bijective analysis. In Proceedings of the twentieth annual ACM-SIAM symposium on Discrete algorithms, pages 1136-1145. SIAM, 2009. URL: https://doi.org/10.1137/1.9781611973068.123.
  2. Luca Becchetti. Modeling locality: A probabilistic analysis of lru and fwf. In Algorithms-ESA 2004: 12th Annual European Symposium, Bergen, Norway, September 14-17, 2004. Proceedings 12, pages 98-109. Springer, 2004. URL: https://doi.org/10.1007/978-3-540-30140-0_11.
  3. Laszlo A. Belady. A study of replacement algorithms for a virtual-storage computer. IBM Systems journal, 5(2):78-101, 1966. URL: https://doi.org/10.1147/sj.52.0078.
  4. Allan Borodin and Ran El-Yaniv. Online computation and competitive analysis. cambridge university press, 2005. Google Scholar
  5. Allan Borodin, Prabhakar Raghavan, Sandy Irani, and Baruch Schieber. Competitive paging with locality of reference. In Proceedings of the twenty-third annual ACM symposium on Theory of computing, pages 249-259, 1991. Google Scholar
  6. Peter J Denning. The working set model for program behavior. Communications of the ACM, 11(5):323-333, 1968. URL: https://doi.org/10.1145/363095.363141.
  7. Reza Dorrigiv and Alejandro López-Ortiz. A survey of performance measures for on-line algorithms. SIGACT News, 36(3):67-81, 2005. URL: http://dl.acm.org/citation.cfm?id=1086670.
  8. Amos Fiat and Anna R Karlin. Randomized and multipointer paging with locality of reference. In Proceedings of the twenty-seventh annual ACM symposium on Theory of computing, pages 626-634, 1995. URL: https://doi.org/10.1145/225058.225280.
  9. Amos Fiat and Manor Mendel. Truly online paging with locality of reference. In Proceedings 38th Annual Symposium on Foundations of Computer Science, pages 326-335. IEEE, 1997. URL: https://doi.org/10.1109/SFCS.1997.646121.
  10. Yi Hao, Alon Orlitsky, and Venkatadheeraj Pichapati. On learning markov chains. Advances in Neural Information Processing Systems, 31, 2018. Google Scholar
  11. De Huang and Xiangyuan Li. Non-asymptotic estimates for markov transition matrices with rigorous error bounds. arXiv preprint arXiv:2408.05963, 2024. Google Scholar
  12. Sandy Irani. Competitive analysis of paging. Online Algorithms: The State of the Art, pages 52-73, 2005. Google Scholar
  13. Sandy Irani, Anna R Karlin, and Steven Phillips. Strongly competitive algorithms for paging with locality of reference. In Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms, pages 228-236, 1992. URL: http://dl.acm.org/citation.cfm?id=139404.139455.
  14. AR Karlin, SJ Phillips, and P Raghavan. Markov paging. In Proceedings of the 33rd Annual Symposium on Foundations of Computer Science, pages 208-217, 1992. Google Scholar
  15. Elias Koutsoupias and Christos H Papadimitriou. Beyond competitive analysis. SIAM Journal on Computing, 30(1):300-317, 2000. URL: https://doi.org/10.1137/S0097539796299540.
  16. Carsten Lund, Steven Phillips, and Nick Reingold. IP over connection-oriented networks and distributional paging. In Proceedings 35th Annual Symposium on Foundations of Computer Science, pages 424-434. IEEE, 1994. URL: https://doi.org/10.1109/SFCS.1994.365674.
  17. Carsten Lund, Steven Phillips, and Nick Reingold. Paging against a distribution and IP networking. Journal of Computer and System Sciences, 58(1):222-231, 1999. URL: https://doi.org/10.1006/jcss.1997.1498.
  18. Thodoris Lykouris and Sergei Vassilvitskii. Competitive caching with machine learned advice. Journal of the ACM (JACM), 68(4):1-25, 2021. URL: https://doi.org/10.1145/3447579.
  19. Mohammad Mahdian, Hamid Nazerzadeh, and Amin Saberi. Online optimization with uncertain information. ACM Transactions on Algorithms (TALG), 8(1):1-29, 2012. URL: https://doi.org/10.1145/2071379.2071381.
  20. Chirag Pabbaraju and Ali Vakilian. New and improved bounds for markov paging. arXiv preprint arXiv:2502.05511, 2025. URL: https://doi.org/10.48550/arXiv.2502.05511.
  21. Tim Roughgarden. CS 369N Beyond Worst-Case Analysis, Lecture Notes 2: Models of Data in Online Paging. https://timroughgarden.org/f11/l2.pdf, 2010.
  22. Daniel D Sleator and Robert E Tarjan. Amortized efficiency of list update and paging rules. Communications of the ACM, 28(2):202-208, 1985. URL: https://doi.org/10.1145/2786.2793.
  23. Eric Torng. A unified analysis of paging and caching. Algorithmica, 20:175-200, 1998. URL: https://doi.org/10.1007/PL00009192.
  24. Geoffrey Wolfer and Aryeh Kontorovich. Statistical estimation of ergodic markov chain kernel over discrete state space. Bernoulli, 27(1):532-553, 2021. Google Scholar
  25. Neal E Young. Bounding the diffuse adversary. In Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms, pages 420-425, 1998. URL: http://dl.acm.org/citation.cfm?id=314613.314772.
  26. Neal E Young. On-line paging against adversarially biased random inputs. Journal of Algorithms, 37(1):218-235, 2000. URL: https://doi.org/10.1006/jagm.2000.1099.
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