Document Open Access Logo

Distributional Online Weighted Paging with Limited Horizon

Authors Yaron Fairstein , Joseph (Seffi) Naor, Tomer Tsachor

PDF

File

Thumbnail PDF
PDF
LIPIcs.APPROX-RANDOM.2024.15.pdf
  • Filesize: 0.82 MB
  • 15 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Caching and paging algorithms
  • Theory of computation → Probabilistic computation
  • Theory of computation → Linear programming
Keywords
  • Online algorithms
  • Caching
  • Stochastic analysis
  • Predictions

Metrics

Abstract

In this work we study the classic problem of online weighted paging with a probabilistic prediction model, in which we are given additional information about the input in the form of distributions over page requests, known as distributional online paging (DOP). This work continues a recent line of research on learning-augmented algorithms that incorporates machine-learning predictions in online algorithms, so as to go beyond traditional worst-case competitive analysis, thus circumventing known lower bounds for online paging. We first provide an efficient online algorithm that achieves a constant factor competitive ratio with respect to the best online algorithm (policy) for weighted DOP that follows from earlier work on the stochastic k-server problem.
Our main contribution concerns the question of whether distributional information over a limited horizon suffices for obtaining a constant competitive factor. To this end, we define in a natural way a new predictive model with limited horizon, which we call Per-Request Stochastic Prediction (PRSP). We show that we can obtain a constant factor competitive algorithm with respect to the optimal online algorithm for this model.

Cite As Get BibTex

Yaron Fairstein, Joseph (Seffi) Naor, and Tomer Tsachor. Distributional Online Weighted Paging with Limited Horizon. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.15

Author Details

Yaron Fairstein
  • Amazon.com, Haifa, Israel
Joseph (Seffi) Naor
  • Computer Science Department, Technion, Haifa, Israel
Tomer Tsachor
  • Computer Science Department, Technion, Haifa, Israel

Funding

  • Naor, Joseph (Seffi): Supported in part by Israel Science Foundation grant 2233/19 and United States - Israel Binational Science Foundation (BSF) grant 2033185.

References

  1. Dimitris Achlioptas, Marek Chrobak, and John Noga. Competitive analysis of randomized paging algorithms. Theor. Comput. Sci., 234(1-2):203-218, 2000. URL: https://doi.org/10.1016/S0304-3975(98)00116-9.
  2. Anna Adamaszek, Artur Czumaj, Matthias Englert, and Harald Räcke. An o(log k)-competitive algorithm for generalized caching. ACM Trans. Algorithms, 15(1), November 2018. URL: https://doi.org/10.1145/3280826.
  3. Susanne Albers. On the influence of lookahead in competitive paging algorithms. Algorithmica, 18(3):283-305, 1997. URL: https://doi.org/10.1007/PL00009158.
  4. Susanne Albers, Sanjeev Arora, and Sanjeev Khanna. Page replacement for general caching problems. In Robert Endre Tarjan and Tandy J. Warnow, editors, Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms, 17-19 January 1999, Baltimore, Maryland, USA, pages 31-40. ACM/SIAM, 1999. URL: http://dl.acm.org/citation.cfm?id=314500.314528.
  5. Algorithms with predictions (ALPS). https://algorithms-with-predictions.github.io/. Accessed: 2022-11-07.
  6. Nikhil Bansal, Niv Buchbinder, and Joseph Naor. Randomized competitive algorithms for generalized caching. SIAM J. Comput., 41(2):391-414, 2012. URL: https://doi.org/10.1137/090779000.
  7. Nikhil Bansal, Niv Buchbinder, and Joseph Seffi Naor. A primal-dual randomized algorithm for weighted paging. Journal of the ACM (JACM), 59(4):19, 2012. Google Scholar
  8. Nikhil Bansal, Christian Coester, Ravi Kumar, Manish Purohit, and Erik Vee. Scale-free allocation, amortized convexity, and myopic weighted paging. CoRR, abs/2011.09076, 2020. URL: https://arxiv.org/abs/2011.09076.
  9. Rakesh D. Barve, Edward F. Grove, and Jeffrey Scott Vitter. Application-controlled paging for a shared cache. SIAM Journal on Computing, 29(4):1290-1303, 2000. URL: https://doi.org/10.1137/S0097539797324278.
  10. A. Blum, M. Furst, and A. Tomkins. What to do with your free time: algorithms for infrequent requests and randomized weighted caching, 1996. Google Scholar
  11. Avrim Blum, Carl Burch, and Adam Kalai. Finely-competitive paging. In 40th Annual Symposium on Foundations of Computer Science, FOCS '99, 17-18 October, 1999, New York, NY, USA, pages 450-458. IEEE Computer Society, 1999. URL: https://doi.org/10.1109/SFFCS.1999.814617.
  12. A. Borodin, S. Irani, P. Raghavan, and B. Schieber. Competitive paging with locality of reference. Journal of Computer and System Sciences, 50(2):244-258, 1995. URL: https://doi.org/10.1006/jcss.1995.1021.
  13. Allan Borodin and Ran El-Yaniv. Online computation and competitive analysis. Cambridge University Press, 1998. Google Scholar
  14. Dany Breslauer. On competitive on-line paging with lookahead. Theor. Comput. Sci., 209(1-2):365-375, 1998. URL: https://doi.org/10.1016/S0304-3975(98)00118-2.
  15. Sébastien Bubeck, Michael B. Cohen, Yin Tat Lee, James R. Lee, and Aleksander Madry. k-server via multiscale entropic regularization. In Ilias Diakonikolas, David Kempe, and Monika Henzinger, editors, Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, Los Angeles, CA, USA, June 25-29, 2018, pages 3-16. ACM, 2018. URL: https://doi.org/10.1145/3188745.3188798.
  16. Niv Buchbinder, Shahar Chen, and Joseph Naor. Competitive analysis via regularization. In Chandra Chekuri, editor, Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, Oregon, USA, January 5-7, 2014, pages 436-444. SIAM, 2014. URL: https://doi.org/10.1137/1.9781611973402.32.
  17. Niv Buchbinder, Joseph Seffi Naor, et al. The design of competitive online algorithms via a primal-dual approach. Foundations and Trendsregistered in Theoretical Computer Science, 3(2-3):93-263, 2009. Google Scholar
  18. Pei Cao, Edward W. Felten, and Kai Li. Application-Controlled file caching policies. In USENIX Summer 1994 Technical Conference (USENIX Summer 1994 Technical Conference), Boston, MA, June 1994. USENIX Association. URL: https://www.usenix.org/conference/usenix-summer-1994-technical-conference/application-controlled-file-caching-policies.
  19. Marek Chrobak and Lawrence L. Larmore. An optimal on-line algorithm for k-servers on trees. SIAM J. Comput., 20(1):144-148, 1991. URL: https://doi.org/10.1137/0220008.
  20. Sina Dehghani, Soheil Ehsani, MohammadTaghi Hajiaghayi, Vahid Liaghat, and Saeed Seddighin. Stochastic k-server: How should uber work? In Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn, and Anca Muscholl, editors, 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, July 10-14, 2017, Warsaw, Poland, volume 80 of LIPIcs, pages 126:1-126:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.ICALP.2017.126.
  21. Guy Even, Moti Medina, and Dror Rawitz. Online generalized caching with varying weights and costs. In Christian Scheideler and Jeremy T. Fineman, editors, Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures, SPAA 2018, Vienna, Austria, July 16-18, 2018, pages 205-212. ACM, 2018. URL: https://doi.org/10.1145/3210377.3210404.
  22. Amos Fiat, Richard M. Karp, Michael Luby, Lyle A. McGeoch, Daniel Dominic Sleator, and Neal E. Young. Competitive paging algorithms. J. Algorithms, 12(4):685-699, 1991. URL: https://doi.org/10.1016/0196-6774(91)90041-V.
  23. Amos Fiat and Manor Mendel. Truly online paging with locality of reference. CoRR, abs/cs/0601127, 2006. URL: https://arxiv.org/abs/cs/0601127.
  24. Peter A. Franaszek and T. J. Wagner. Some distribution-free aspects of paging algorithm performance. J. ACM, 21(1):31-39, 1974. Google Scholar
  25. Anupam Gupta, Ravishankar Krishnaswamy, Amit Kumar, and Debmalya Panigrahi. Elastic caching. In Timothy M. Chan, editor, Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019, pages 143-156. SIAM, 2019. URL: https://doi.org/10.1137/1.9781611975482.10.
  26. Anupam Gupta, Amit Kumar, and Debmalya Panigrahi. Caching with time windows. In Konstantin Makarychev, Yury Makarychev, Madhur Tulsiani, Gautam Kamath, and Julia Chuzhoy, editors, Proccedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020, Chicago, IL, USA, June 22-26, 2020, pages 1125-1138. ACM, 2020. URL: https://doi.org/10.1145/3357713.3384277.
  27. Sandy Irani. Competitive analysis of paging. In Amos Fiat and Gerhard J. Woeginger, editors, Online Algorithms, The State of the Art (the book grow out of a Dagstuhl Seminar, June 1996), volume 1442 of Lecture Notes in Computer Science, pages 52-73. Springer, 1996. URL: https://doi.org/10.1007/BFb0029564.
  28. Sandy Irani. Page replacement with multi-size pages and applications to web caching. In Frank Thomson Leighton and Peter W. Shor, editors, Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing, El Paso, Texas, USA, May 4-6, 1997, pages 701-710. ACM, 1997. URL: https://doi.org/10.1145/258533.258666.
  29. Sandy Irani. Randomized weighted caching with two page weights. Algorithmica, 32(4):624-640, 2002. URL: https://doi.org/10.1007/s00453-001-0095-6.
  30. Sandy Irani, Anna R. Karlin, and Steven Phillips. Strongly competitive algorithms for paging with locality of reference. SIAM Journal on Computing, 25(3):477-497, 1996. URL: https://doi.org/10.1137/S0097539792236353.
  31. Zhihao Jiang, Debmalya Panigrahi, and Kevin Sun. Online algorithms for weighted paging with predictions. In Artur Czumaj, Anuj Dawar, and Emanuela Merelli, editors, 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, July 8-11, 2020, Saarbrücken, Germany (Virtual Conference), volume 168 of LIPIcs, pages 69:1-69:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ICALP.2020.69.
  32. Anna R. Karlin, Steven J. Phillips, and Prabhakar Raghavan. Markov paging (extended abstract). In 33rd Annual Symposium on Foundations of Computer Science, Pittsburgh, Pennsylvania, USA, 24-27 October 1992, pages 208-217. IEEE Computer Society, 1992. URL: https://doi.org/10.1109/SFCS.1992.267771.
  33. Ravi Kumar, Manish Purohit, Zoya Svitkina, and Erik Vee. Interleaved caching with access graphs. In Proceedings of the Thirty-First Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '20, pages 1846-1858, USA, 2020. Society for Industrial and Applied Mathematics. Google Scholar
  34. Carsten Lund, Steven J. Phillips, and Nick Reingold. Paging against a distribution and IP networking. J. Comput. Syst. Sci., 58(1):222-232, 1999. URL: https://doi.org/10.1006/jcss.1997.1498.
  35. Thodoris Lykouris and Sergei Vassilvitskii. Competitive caching with machine learned advice. In Jennifer G. Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning, ICML 2018, Stockholmsmässan, Stockholm, Sweden, July 10-15, 2018, volume 80 of Proceedings of Machine Learning Research, pages 3302-3311. PMLR, 2018. URL: http://proceedings.mlr.press/v80/lykouris18a.html.
  36. Lyle A. McGeoch and Daniel Dominic Sleator. A strongly competitive randomized paging algorithm. Algorithmica, 6(6):816-825, 1991. URL: https://doi.org/10.1007/BF01759073.
  37. Gerald S. Shedler and C. Tung. Locality in page reference strings. SIAM J. Comput., 1(3):218-241, 1972. Google Scholar
  38. Daniel Dominic Sleator and Robert Endre Tarjan. Amortized efficiency of list update and paging rules. Commun. ACM, 28(2):202-208, 1985. URL: https://doi.org/10.1145/2786.2793.
  39. Neal Young. Competitive paging and dual-guided on-line weighted caching and matching algorithms. Princeton University, 1991. Google Scholar
  40. Neal E. Young. On-line caching as cache size varies. In Alok Aggarwal, editor, Proceedings of the Second Annual ACM/SIGACT-SIAM Symposium on Discrete Algorithms, 28-30 January 1991, San Francisco, California, USA, pages 241-250. ACM/SIAM, 1991. URL: http://dl.acm.org/citation.cfm?id=127787.127832.
  41. Neal E. Young. The k-server dual and loose competitiveness for paging. Algorithmica, 11(6):525-541, 1994. URL: https://doi.org/10.1007/BF01189992.
  42. Neal E. Young. On-line file caching. In Symposium on Discrete algorithms, pages 82-86, 1998. Google Scholar
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact