Online Demand Scheduling with Failovers

Authors Konstantina Mellou, Marco Molinaro, Rudy Zhou



PDF
Thumbnail PDF

File

LIPIcs.ICALP.2023.92.pdf
  • Filesize: 0.89 MB
  • 20 pages

Document Identifiers

Author Details

Konstantina Mellou
  • Microsoft Research, Redmond, WA, USA
Marco Molinaro
  • Microsoft Research, Redmond, WA, USA
  • PUC-Rio de Janeiro, Brazil
Rudy Zhou
  • Carnegie Mellon University, Pittsburgh, PA, USA

Acknowledgements

We thank the anonymous reviewers for their valuable suggestions. We also thank Alok Gautam Kumbhare and Ishai Menache for useful discussions.

Cite As Get BibTex

Konstantina Mellou, Marco Molinaro, and Rudy Zhou. Online Demand Scheduling with Failovers. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 92:1-92:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ICALP.2023.92

Abstract

Motivated by cloud computing applications, we study the problem of how to optimally deploy new hardware subject to both power and robustness constraints. To model the situation observed in large-scale data centers, we introduce the Online Demand Scheduling with Failover problem. There are m identical devices with capacity constraints. Demands come one-by-one and, to be robust against a device failure, need to be assigned to a pair of devices. When a device fails (in a failover scenario), each demand assigned to it is rerouted to its paired device (which may now run at increased capacity). The goal is to assign demands to the devices to maximize the total utilization subject to both the normal capacity constraints as well as these novel failover constraints. These latter constraints introduce new decision tradeoffs not present in classic assignment problems such as the Multiple Knapsack problem and AdWords.
In the worst-case model, we design a deterministic ≈ 1/2-competitive algorithm, and show this is essentially tight. To circumvent this constant-factor loss, which represents substantial capital losses for big cloud providers, we consider the stochastic arrival model, where all demands come i.i.d. from an unknown distribution. In this model we design an algorithm that achieves sub-linear additive regret (i.e. as OPT or m increases, the multiplicative competitive ratio goes to 1). This requires a combination of different techniques, including a configuration LP with a non-trivial post-processing step and an online monotone matching procedure introduced by Rhee and Talagrand.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • online algorithms
  • approximation algorithms
  • resource allocation

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Sara Ahmadian and Zachary Friggstad. Further approximations for demand matching: Matroid constraints and minor-closed graphs. In 44th International Colloquium on Automata, Languages, and Programming, ICALP, 2017. URL: https://doi.org/10.4230/LIPIcs.ICALP.2017.55.
  2. János Balogh, József Békési, György Dósa, Leah Epstein, and Asaf Levin. A New and Improved Algorithm for Online Bin Packing. In 26th Annual European Symposium on Algorithms (ESA), 2018. URL: https://doi.org/10.4230/LIPIcs.ESA.2018.5.
  3. Stéphane Boucheron, Gábor Lugosi, and Pascal Massart. Concentration inequalities: A nonasymptotic theory of independence. Oxford university press, 2013. Google Scholar
  4. Chandra Chekuri and Sanjeev Khanna. A polynomial time approximation scheme for the multiple knapsack problem. SIAM Journal on Computing, 35(3):713-728, 2005. URL: https://doi.org/10.1137/S0097539700382820.
  5. Janos 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 (JACM), 53(1):1-65, 2006. Google Scholar
  6. Anupam Gupta and Jochen Könemann. Approximation algorithms for network design: A survey. Surveys in Operations Research and Management Science, 16(1):3-20, 2011. URL: https://doi.org/10.1016/j.sorms.2010.06.001.
  7. Anupam Gupta and Marco Molinaro. How the experts algorithm can help solve lps online. Mathematics of Operations Research, 41(4):1404-1431, 2016. URL: https://doi.org/10.1287/moor.2016.0782.
  8. Varun Gupta and Ana Radovanović. Interior-point-based online stochastic bin packing. Operations Research, 68(5):1474-1492, 2020. Google Scholar
  9. Rebecca Hoberg and Thomas Rothvoss. A logarithmic additive integrality gap for bin packing. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, 2017. Google Scholar
  10. Narendra Karmarkar and Richard M. Karp. An efficient approximation scheme for the one-dimensional bin-packing problem. In 23rd Annual Symposium on Foundations of Computer Science (SFCS 1982), pages 312-320, 1982. URL: https://doi.org/10.1109/SFCS.1982.61.
  11. Madhukar Korupolu, Adam Meyerson, Rajmohan Rajaraman, and Brian Tagiku. Coupled and k-sided placements: Generalizing generalized assignment. Math. Program., 154(1–2):493-514, December 2015. URL: https://doi.org/10.1007/s10107-015-0930-1.
  12. Lap-Chi Lau, R. Ravi, and Mohit Singh. Iterative Methods in Combinatorial Optimization. Cambridge University Press, USA, 1st edition, 2011. Google Scholar
  13. Shang Liu and Xiaocheng Li. Online bin packing with known T. arXiv preprint arXiv:2112.03200, 2021. Google Scholar
  14. Aranyak Mehta, Amin Saberi, Umesh Vazirani, and Vijay Vazirani. Adwords and generalized online matching. J. ACM, 54(5):22-es, October 2007. URL: https://doi.org/10.1145/1284320.1284321.
  15. Wansoo T. Rhee and Michel Talagrand. Optimal bin packing with items of random sizes II. SIAM Journal on Computing, 18(1):139-151, 1989. URL: https://doi.org/10.1137/0218009.
  16. Wansoo T Rhee and Michel Talagrand. On-line bin packing of items of random sizes, II. SIAM Journal on Computing, 22(6):1251-1256, 1993. Google Scholar
  17. Thomas Rothvoß. The entropy rounding method in approximation algorithms. In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, 2012. Google Scholar
  18. David B Shmoys and Éva Tardos. An approximation algorithm for the generalized assignment problem. Mathematical programming, 62(1):461-474, 1993. Google Scholar
  19. Chaojie Zhang, Alok Gautam Kumbhare, Ioannis Manousakis, Deli Zhang, Pulkit A Misra, Rod Assis, Kyle Woolcock, Nithish Mahalingam, Brijesh Warrier, David Gauthier, et al. Flex: High-availability datacenters with zero reserved power. In ACM/IEEE 48th Annual International Symposium on Computer Architecture (ISCA), 2021. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail