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Online Bin Covering with Frequency Predictions

Authors Magnus Berg , Shahin Kamali

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ACM Subject Classification
  • Theory of computation → Packing and covering problems
  • Theory of computation → Online learning algorithms
  • Theory of computation → Online algorithms
Keywords
  • Bin Covering
  • Online Algorithms with Predictions
  • PAC Learning
  • Learning-Augmented Algorithms

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Abstract

We study the bin covering problem where a multiset of items from a fixed set S ⊆ (0,1] must be split into disjoint subsets while maximizing the number of subsets whose contents sum to at least 1. We focus on the online discrete variant, where S is finite, and items arrive sequentially. In the purely online setting, we show that the competitive ratios of best deterministic (and randomized) algorithms converge to 1/2 for large S, similar to the continuous setting. Therefore, we consider the problem under the prediction setting, where algorithms may access a vector of frequencies predicting the frequency of items of each size in the instance. In this setting, we introduce a family of online algorithms that perform near-optimally when the predictions are correct. Further, we introduce a second family of more robust algorithms that presents a tradeoff between the performance guarantees when the predictions are perfect and when predictions are adversarial. Finally, we consider a stochastic setting where items are drawn independently from any fixed but unknown distribution of S. Using results from the PAC-learnability of probabilities in discrete distributions, we introduce a purely online algorithm whose average-case performance is near-optimal with high probability for all finite sets S and all distributions of S.

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Magnus Berg and Shahin Kamali. Online Bin Covering with Frequency Predictions. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SWAT.2024.10

Author Details

Magnus Berg
  • University of Southern Denmark, Odense, Denmark
Shahin Kamali
  • York University, Toronto, Canada

Funding

  • Berg, Magnus: Supported in part by the Independent Research Fund Denmark, Natural Sciences, grant DFF-0135-00018B and in part by the Innovation Fund Denmark, grant 9142-00001B, Digital Research Centre Denmark, project P40: Online Algorithms with Predictions.
  • Kamali, Shahin: Supported in part by Natural Sciences and Engineering Research Council of Canada (NSERC) [funding reference number DGECR-2018-00059].

References

  1. Algorithms with predictions. URL: https://algorithms-with-predictions.github.io/. Accessed: 2024-01-26.
  2. Spyros Angelopoulos, Christoph Dürr, Shendan Jin, Shahin Kamali, and Marc P. Renault. Online computation with untrusted advice. In 11th Innovations in Theoretical Computer Science Conference (ITCS), pages 52:1-52:15. Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ITCS.2020.52.
  3. Spyros Angelopoulos and Shahin Kamali. Contract scheduling with predictions. J. Artif. Intell. Res., 77:395-426, 2023. Google Scholar
  4. Spyros Angelopoulos, Shahin Kamali, and Kimia Shadkami. Online bin packing with predictions. Journal of Artificial Intelligence Research, 78:1111-1141, 2023. URL: https://doi.org/10.1613/jair.1.14820.
  5. Susan F. Assmann, David S. Johnson, Daniel J. Kleitman, and Josepth Y.-T. Leung. On a dual version of the one-dimensional packing problem. Journal of Algorithms, 5:502-525, 1984. URL: https://doi.org/10.1016/0196-6774(84)90004-X.
  6. Siddhartha Banerjee and Daniel Freund. Uniform loss algorithms for online stochastic decision-making with applications to bin packing. In Abstracts of the 2020 SIGMETRICS, pages 1-2. ACM, 2020. URL: https://doi.org/10.1145/3393691.3394224.
  7. Magnus Berg, Joan Boyar, Lene M. Favrholdt, and Kim S. Larsen. Online minimum spanning trees with weight predictions. In Algorithms and Data Structures (WADS), pages 136-148. Springer, Cham, 2023. URL: https://doi.org/10.1007/978-3-031-38906-1_10.
  8. Magnus Berg and Shahin Kamali. Online bin covering with frequency predictions, 2024. arXiv:2401.14881. Google Scholar
  9. Allan Borodin and Ran El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, New York, NY, USA, 1998. Google Scholar
  10. Joan Boyar, Lene M. Favrholdt, Shahin Kamali, and Kim S. Larsen. Online bin covering with advice. Algorithmica, 83:795-821, 2021. URL: https://doi.org/10.1007/s00453-020-00728-0.
  11. Joan Boyar, Lene M. Favrholdt, Shahin Kamali, and Kim S. Larsen. Online interval scheduling with predictions. In 18th International Symposium on Algorithms and Data Structures (WADS), volume 14079, pages 193-207, 2023. Google Scholar
  12. Andrej Brodnik, Bengt J. Nilsson, and Gordana Vujovic. Online bin covering with exact parameter advice. arXiv:2309.13647, 2023. URL: https://doi.org/10.48550/arXiv.2309.13647.
  13. Clément L. Canonne. A short note on learning discrete distributions. arXiv:2002.11457, 2020. URL: https://doi.org/10.48550/arXiv.2002.11457.
  14. János Csirik, J. B. G. Frenk, Martine Labbé, and Shuzhong Zhang. Two simple algorithms for bin covering. Acta Cybernetica, 14:13-25, 1999. Google Scholar
  15. János Csirik, David S. Johnson, and Claire Kenyon. Better approximation algorithms for bin covering. In 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 557-566. SIAM, 2001. Google Scholar
  16. János Csirik, David S. Johnson, Claire Kenyon, James B. Orlin, Peter W. Shor, and Richard R. Weber. On the sum-of-squares algorithm for bin packing. Journal of the ACM, 53:1-65, 2006. URL: https://doi.org/10.1145/1120582.1120583.
  17. János Csirik, David S. Johnson, Claire Kenyon, Peter W. Shor, and Richard R. Weber. A self organizing bin packing heuristic. In Algorithms Engeneering and Experimentation (ALENEX), pages 250-269. Springer, 1999. URL: https://doi.org/10.1007/3-540-48518-X_15.
  18. János Csirik and Vilmos Totik. Online algorithms for a dual version of bin packing. Discrete Applied Mathematics, 21:163-167, 1988. URL: https://doi.org/10.1016/0166-218X(88)90052-2.
  19. János Csirik and Gerhard H. Woeginger. On-line packing and covering problems. In Online Algorithms, pages 147-177. Springer, Berlin, Heidelberg, 2005. URL: https://doi.org/10.1007/BFb0029568.
  20. Leah Epstein. Online variable sized covering. Information and Computation, 171:294-305, 2001. URL: https://doi.org/10.1006/inco.2001.3087.
  21. Anupam Gupta, Gregory Kehne, and Roie Levin. Random order online set cover is as easy as offline. In 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021, Denver, CO, USA, February 7-10, 2022, pages 1253-1264. IEEE, 2021. URL: https://doi.org/10.1109/FOCS52979.2021.00122.
  22. Klaus Jensen and Roberto Solis-Oba. An asymptotic fully polynomial time approximation scheme for bin covering. Theoretical Computer Science, 306:543-551, 2003. URL: https://doi.org/10.1016/S0304-3975(03)00363-3.
  23. Dennis Komm. An Introduction to Online Computation: Determinism, Randomization, Advice. Springer Cham, Switzerland, 2016. URL: https://doi.org/10.1007/978-3-319-42749-2.
  24. Thodoris Lykouris and Sergei Vassilvitskii. Competitive caching with machine learned advice. Journal of the ACM, 68:1-25, 2021. URL: https://doi.org/10.1145/3447579.
  25. Manish Purohit, Zoya Svitkina, and Ravi Kumar. Improving online algorithms via ml predictions. In 32nd Conference on Neural Information Processing Systems (NeurIPS), pages 9684-9693. Curran Associates, Inc., 2018. Google Scholar
  26. Shai Shalev-Shwartz and Shai Ben-David. Understanding Machine Learning Theory: From Theory to Algorithms. Cambridge University Press, Cambridge, England, 2014. URL: https://doi.org/10.1017/CBO9781107298019.
  27. Alexander Wei and Fred Zhang. Optimal robustness-consistency trade-offs for learning-augmented online algorithms. In 34th Conference on Neural Information Processing Systems (NeurIPS), pages 8042-8053. Curran Associates, Inc., 2020. Google Scholar
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