Skip to main content
SpringerLink
Log in

Online Interval Scheduling with Predictions

  • Conference paper
  • First Online:
Algorithms and Data Structures (WADS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14079))

Included in the following conference series:

  • 649 Accesses

Abstract

In online interval scheduling, the input is an online sequence of intervals, and the goal is to accept a maximum number of non-overlapping intervals. In the more general disjoint path allocation problem, the input is a sequence of requests, each involving a pair of vertices of a known graph, and the goal is to accept a maximum number of requests forming edge-disjoint paths between accepted pairs. These problems have been studied under extreme settings without information about the input or with error-free advice. We study an intermediate setting with a potentially erroneous prediction that specifies the set of intervals/requests forming the input sequence. For both problems, we provide tight upper and lower bounds on the competitive ratios of online algorithms as a function of the prediction error. For disjoint path allocation, our results rule out the possibility of obtaining a better competitive ratio than that of a simple algorithm that fully trusts predictions, whereas, for interval scheduling, we develop a superior algorithm. We also present asymptotically tight trade-offs between consistency (competitive ratio with error-free predictions) and robustness (competitive ratio with adversarial predictions) of interval scheduling algorithms. Finally, we provide experimental results on real-world scheduling workloads that confirm our theoretical analysis.

The first, second, and fourth authors were supported in part by the Danish Council for Independent Research 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.

The third author was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Algorithms with predictions. https://algorithms-with-predictions.github.io/. Accessed 19 Feb 2023

  2. Interval scheduling with prediction. https://github.com/shahink84/IntervalSchedulingWithPrediction. Accessed 19 Feb 2023

  3. Angelopoulos, S., Dürr, C., Jin, S., Kamali, S., Renault, M.: Online computation with untrusted advice. In: Proceedings of the ITCS. LIPIcs, vol. 151, pp. 52:1–52:15 (2020)

    Google Scholar 

  4. Angelopoulos, S., Kamali, S., Shadkami, K.: Online bin packing with predictions. In: Proceedings of the IJCAI, pp. 4574–4580 (2022)

    Google Scholar 

  5. Angelopoulos, S., Kamali, S., Zhang, D.: Online search with best-price and query-based predictions. In: Proceedings of the AAAI, pp. 9652–9660 (2023)

    Google Scholar 

  6. Angelopoulos, S., Kamali, S.: Contract scheduling with predictions. In: Proceedings of the AAAI, pp. 11726–11733. AAAI Press (2021)

    Google Scholar 

  7. Angelopoulos, S., Arsénio, D., Kamali, S.: Competitive sequencing with noisy advice. CoRR abs/2111.05281 (2021)

    Google Scholar 

  8. Antoniadis, A., et al.: Paging with succinct predictions. In: Proceedings of the ICML (2023, to appear)

    Google Scholar 

  9. Antoniadis, A., Gouleakis, T., Kleer, P., Kolev, P.: Secretary and online matching problems with machine learned advice. In: Proceedings of the NeurIPS (2020)

    Google Scholar 

  10. Awerbuch, B., Bartal, Y., Fiat, A., Rosén, A.: Competitive non-preemptive call control. In: Proceedings of the SODA, pp. 312–320 (1994)

    Google Scholar 

  11. Azar, Y., Leonardi, S., Touitou, N.: Flow time scheduling with uncertain processing time. In: Proceedings of the STOC, pp. 1070–1080 (2021)

    Google Scholar 

  12. Azar, Y., Panigrahi, D., Touitou, N.: Online graph algorithms with predictions. In: Proceedings of the SODA, pp. 35–66 (2022)

    Google Scholar 

  13. Balkanski, E., Gkatzelis, V., Tan, X.: Strategyproof scheduling with predictions. In: Proceedings of the ITCS. LIPIcs, vol. 251, pp. 11:1–11:22 (2023)

    Google Scholar 

  14. Bampis, E., Dogeas, K., Kononov, A.V., Lucarelli, G., Pascual, F.: Scheduling with untrusted predictions. In: Proceedings of the IJCAI, pp. 4581–4587 (2022)

    Google Scholar 

  15. Banerjee, S., Cohen-Addad, V., A., Li, Z.: Graph searching with predictions. In: Proceedings of the ITCS. LIPIcs, vol. 251, pp. 12:1–12:24 (2023)

    Google Scholar 

  16. Barhum, K., Böckenhauer, H.-J., Forišek, M., Gebauer, H., Hromkovič, J., Krug, S., Smula, J., Steffen, B.: On the power of advice and randomization for the disjoint path allocation problem. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds.) SOFSEM 2014. LNCS, vol. 8327, pp. 89–101. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04298-5_9

    Chapter  MATH  Google Scholar 

  17. Berg, M., Boyar, J., Favrholdt, L.M., Larsen, K.S.: Online interval scheduling with predictions. ArXiv (2023). arXiv:2302.13701. To appear in 18th WADS, 2023

  18. Böckenhauer, H., Benz, N.C., Komm, D.: Call admission problems on trees. Theor. Comput. Sci. 922, 410–423 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  19. Böckenhauer, H., Komm, D., Wegner, R.: Call admission problems on grids with advice. Theor. Comput. Sci. 918, 77–93 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  20. Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  21. Boyar, J., Favrholdt, L.M., Larsen, K.S.: Online unit profit knapsack with untrusted predictions. In: Proceedings of the SWAT. LIPIcs, vol. 227, pp. 20:1–20:17 (2022)

    Google Scholar 

  22. Boyar, J., Favrholdt, L.M., Kudahl, C., Mikkelsen, J.W.: The advice complexity of a class of hard online problems. Theory Comput. Syst. 61(4), 1128–1177 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  23. Chapin, S.J., et al.: Benchmarks and standards for the evaluation of parallel job schedulers. In: Feitelson, D.G., Rudolph, L. (eds.) JSSPP 1999. LNCS, vol. 1659, pp. 67–90. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-47954-6_4

    Chapter  Google Scholar 

  24. Chen, J.Y., et al.: Triangle and four cycle counting with predictions in graph streams. In: Proceedings of the ICLR (2022)

    Google Scholar 

  25. Chen, J.Y., Silwal, S., Vakilian, A., Zhang, F.: Faster fundamental graph algorithms via learned predictions. In: Proceedings of the ICML. PLMR, vol. 162, pp. 3583–3602 (2022)

    Google Scholar 

  26. Wagner, D., Weihe, K.: A linear-time algorithm for edge-disjoint paths in planar graphs. Combinatorica 15, 135–150 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  27. Eberle, F., Lindermayr, A., Megow, N., Nölke, L., Schlöter, J.: Robustification of online graph exploration methods. In: Proceedings of the AAAI, pp. 9732–9740 (2022)

    Google Scholar 

  28. Even, S., Itai, A., Shamir, A.: On the complexity of timetable and multicommodity flow problems. SIAM J. Comput. 5(4), 691–703 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  29. Frank, A.: Edge-disjoint paths in planar graphs. J. Combin. Theory Ser. B 39, 164–178 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  30. Garg, N., Vazirani, V.V., Yannakakis, M.: Primal-dual approximation algorithms for integral flow and multicut in trees. Algorithmica 18, 3–20 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  31. Gebauer, H., Komm, D., Královič, R., Královič, R., Smula, J.: Disjoint path allocation with sublinear advice. In: Xu, D., Du, D., Du, D. (eds.) COCOON 2015. LNCS, vol. 9198, pp. 417–429. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21398-9_33

    Chapter  Google Scholar 

  32. Im, S., Kumar, R., Qaem, M.M., Purohit, M.: Non-clairvoyant scheduling with predictions. In: Proceedings of the SPAA, pp. 285–294 (2021)

    Google Scholar 

  33. Im, S., Kumar, R., Qaem, M.M., Purohit, M.: Online knapsack with frequency predictions. In: Proceedings of the NeurIPS, pp. 2733–2743 (2021)

    Google Scholar 

  34. Matsumoto, K., Nishizeki, T., Saito, N.: An efficient algorithm for finding multi-commodity flows in planar networks. SIAM J. Comput. 14(2), 289–302 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  35. Kolen, A.W., Lenstra, J.K., Papadimitriou, C.H., Spieksma, F.C.: Interval scheduling: a survey. Nav. Res. Logist. 54(5), 530–543 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  36. Lattanzi, S., Lavastida, T., Moseley, B., Vassilvitskii, S.: Online scheduling via learned weights. In: Proceedings of the SODA, pp. 1859–1877 (2020)

    Google Scholar 

  37. Lavastida, T., Moseley, B., Ravi, R., Xu, C.: Learnable and instance-robust predictions for online matching, flows and load balancing. In: Proceedings of the ESA. LIPIcs, vol. 204, pp. 59:1–59:17 (2021)

    Google Scholar 

  38. Lavastida, T., Moseley, B., Ravi, R., Xu, C.: Using predicted weights for ad delivery. In: Proceedings of the ACDA, pp. 21–31 (2021)

    Google Scholar 

  39. Lee, R., Maghakian, J., Hajiesmaili, M., Li, J., Sitaraman, R.K., Liu, Z.: Online peak-aware energy scheduling with untrusted advice. In: Proceedings of the e-Energy, pp. 107–123 (2021)

    Google Scholar 

  40. Lykouris, T., Vassilvitskii, S.: Competitive caching with machine learned advice. In: Proceedings of the ICML. PMLR, vol. 80, pp. 3302–3311 (2018)

    Google Scholar 

  41. Mitzenmacher, M., Vassilvitskii, S.: Algorithms with predictions. In: Roughgarden, T. (ed.) Beyond the Worst-Case Analysis of Algorithms, pp. 646–662. Cambridge University Press (2020)

    Google Scholar 

  42. Nishizeki, T., Vygen, J., Zhou, X.: The edge-disjoint paths problem is NP-complete for series-parallel graphs. Discret. Appl. Math. 115(1–3), 177–186 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  43. Purohit, M., Svitkina, Z., Kumar, R.: Improving online algorithms via ML predictions. In: Proceedings of the NeurIPS, pp. 9661–9670 (2018)

    Google Scholar 

  44. Rohatgi, D.: Near-optimal bounds for online caching with machine learned advice. In: Proceedings of the SODA, pp. 1834–1845 (2020)

    Google Scholar 

  45. Wei, A., Zhang, F.: Optimal robustness-consistency trade-offs for learning-augmented online algorithms. In: Proceedings of the NeurIPS (2020)

    Google Scholar 

  46. Wei, A.: Better and simpler learning-augmented online caching. In: Proceedings of the APPROX/RANDOM. LIPIcs, vol. 176, pp. 60:1–60:17 (2020)

    Google Scholar 

  47. Zeynali, A., Sun, B., Hajiesmaili, M., Wierman, A.: Data-driven competitive algorithms for online knapsack and set cover. In: Proceedings of the AAAI, pp. 10833–10841 (2021)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Southern Denmark, Odense, Denmark

    Joan Boyar, Lene M. Favrholdt & Kim S. Larsen

  2. York University, Toronto, Canada

    Shahin Kamali

Authors
  1. Joan Boyar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lene M. Favrholdt
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shahin Kamali
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kim S. Larsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kim S. Larsen .

Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, ON, Canada

    Pat Morin

  2. University of California, Santa Barbara, CA, USA

    Subhash Suri

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Boyar, J., Favrholdt, L.M., Kamali, S., Larsen, K.S. (2023). Online Interval Scheduling with Predictions. In: Morin, P., Suri, S. (eds) Algorithms and Data Structures. WADS 2023. Lecture Notes in Computer Science, vol 14079. Springer, Cham. https://doi.org/10.1007/978-3-031-38906-1_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-38906-1_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-38905-4

  • Online ISBN: 978-3-031-38906-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation