Online Balanced Allocation of Dynamic Components

Authors Rajmohan Rajaraman, Omer Wasim



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Author Details

Rajmohan Rajaraman
  • Northeastern University, Boston, MA, USA
Omer Wasim
  • Northeastern University, Boston, MA, USA

Acknowledgements

This work was partially supported by NSF award CCF-2335187.

Cite As Get BibTex

Rajmohan Rajaraman and Omer Wasim. Online Balanced Allocation of Dynamic Components. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 81:1-81:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.81

Abstract

We introduce Online Balanced Allocation of Dynamic Components (OBADC), a problem motivated by the practical challenge of dynamic resource allocation for large-scale distributed applications. In OBADC, we need to allocate a dynamic set of at most k𝓁 vertices (representing processes) in 𝓁 > 0 clusters. We consider an over-provisioned setup in which each cluster can hold at most k(1+ε) vertices, for an arbitrary constant ε > 0. The communication requirements among the vertices are modeled by the notion of a dynamically changing component, which is a subset of vertices that need to be co-located in the same cluster. At each time t, a request r_t of one of the following types arrives:  
1) insertion of a vertex v forming a singleton component v at unit cost. 
2) merge of (u,v) requiring that the components containing u and v be merged and co-located thereafter. 
3) deletion of an existing vertex v at zero cost.  Before serving any request, an algorithm can migrate vertices from one cluster to another, at a unit migration cost per vertex. We seek an online algorithm to minimize the total migration cost incurred for an arbitrary request sequence σ = (r_t)_{t > 0}, while simultaneously minimizing the number of clusters utilized. We analyze competitiveness with respect to an optimal clairvoyant offline algorithm with identical (over-provisioned) capacity constraints. 
We give an O(log k)-competitive algorithm for OBADC, and a matching lower-bound. The number of clusters utilized by our algorithm is always within a (2+ε) factor of the minimum. Furthermore, in a resource augmented setting where the optimal offline algorithm is constrained to capacity k per cluster, our algorithm obtains O(log k) competitiveness and utilizes a number of clusters within (1+ε) factor of the minimum.
We also consider OBADC in the context of machine-learned predictions, where for each newly inserted vertex v at time t: i) with probability η > 0, the set of vertices (that exist at time t) in the component of v is revealed and, ii) with probability 1-η, no information is revealed. For OBADC with predictions, we give a O(1)-consistent and O(min(log 1/(η), log k))-robust algorithm.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • online algorithms
  • competitive ratio
  • algorithms with predictions

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References

  1. Khaled Almi'ani, Young Choon Lee, and Bernard Mans. Resource demand aware scheduling for workflows in clouds. In 2017 IEEE 16th International Symposium on Network Computing and Applications (NCA), pages 1-5. IEEE, 2017. Google Scholar
  2. Chen Avin, Marcin Bienkowski, Andreas Loukas, Maciej Pacut, and Stefan Schmid. Dynamic balanced graph partitioning. SIAM Journal on Discrete Mathematics, 34(3):1791-1812, 2020. URL: https://doi.org/10.1137/17M1158513.
  3. Yossi Azar, Chay Machluf, Boaz Patt-Shamir, and Noam Touitou. Competitive Vertex Recoloring. In Mikołaj Bojańczyk, Emanuela Merelli, and David P. Woodruff, editors, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022), volume 229 of Leibniz International Proceedings in Informatics (LIPIcs), pages 13:1-13:20, Dagstuhl, Germany, 2022. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ICALP.2022.13.
  4. Marcin Bienkowski, Martin Böhm, Martin Koutecký, Thomas Rothvoß, Jiří Sgall, and Pavel Veselý. Improved analysis of online balanced clustering. In Approximation and Online Algorithms: 19th International Workshop, WAOA 2021, Lisbon, Portugal, September 6–10, 2021, Revised Selected Papers, pages 224-233, Berlin, Heidelberg, 2021. Springer-Verlag. URL: https://doi.org/10.1007/978-3-030-92702-8_14.
  5. Jan van den Brand, Sebastian Forster, Yasamin Nazari, and Adam Polak. On dynamic graph algorithms with predictions. In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 3534-3557. SIAM, 2024. URL: https://doi.org/10.1137/1.9781611977912.126.
  6. Prasad Calyam, Sripriya Seetharam, Baisravan Homchaudhuri, and Manish Kumar. Resource defragmentation using market-driven allocation in virtual desktop clouds. In 2015 IEEE International Conference on Cloud Engineering, pages 246-255. IEEE, 2015. URL: https://doi.org/10.1109/IC2E.2015.37.
  7. Jiuxin Cao, Zhuo Ma, Jue Xie, Xiangying Zhu, Fang Dong, and Bo Liu. Towards tenant demand-aware bandwidth allocation strategy in cloud datacenter. Future Generation Computer Systems, 105:904-915, 2020. URL: https://doi.org/10.1016/J.FUTURE.2017.06.005.
  8. Vincent Cohen-Addad, Tommaso d'Orsi, Anupam Gupta, Euiwoong Lee, and Debmalya Panigrahi. Max-cut with epsilon-accurate predictions. arXiv preprint arXiv:2402.18263, 2024. Google Scholar
  9. Hancong Duan, Chao Chen, Geyong Min, and Yu Wu. Energy-aware scheduling of virtual machines in heterogeneous cloud computing systems. Future Generation Computer Systems, 74:142-150, 2017. URL: https://doi.org/10.1016/J.FUTURE.2016.02.016.
  10. Tobias Forner, Harald Räcke, and Stefan Schmid. Online balanced repartitioning of dynamic communication patterns in polynomial time. In Symposium on Algorithmic Principles of Computer Systems (APOCS), pages 40-54, 2021. URL: https://doi.org/10.1137/1.9781611976489.4.
  11. Anupam Gupta, Debmalya Panigrahi, Bernardo Subercaseaux, and Kevin Sun. Augmenting online algorithms with ε-accurate predictions. Advances in neural information processing systems, 35:2115-2127, 2022. Google Scholar
  12. Sijin He, Li Guo, and Yike Guo. Real time elastic cloud management for limited resources. In 2011 IEEE 4th International Conference on Cloud Computing, pages 622-629. IEEE, 2011. URL: https://doi.org/10.1109/CLOUD.2011.47.
  13. Monika Henzinger, Stefan Neumann, Harald Räcke, and Stefan Schmid. Tight Bounds for Online Graph Partitioning, pages 2799-2818. Society for Industrial and Applied Mathematics, USA, 2021. Google Scholar
  14. Monika Henzinger, Stefan Neumann, and Stefan Schmid. Efficient distributed workload (re-)embedding. In Abstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS '19, pages 43-44, New York, NY, USA, 2019. Association for Computing Machinery. URL: https://doi.org/10.1145/3309697.3331503.
  15. 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.
  16. Zoltán Ádám Mann. Allocation of virtual machines in cloud data centers—a survey of problem models and optimization algorithms. Acm Computing Surveys (CSUR), 48(1):1-34, 2015. URL: https://doi.org/10.1145/2797211.
  17. Suhib Bani Melhem, Anjali Agarwal, Nishith Goel, and Marzia Zaman. Markov prediction model for host load detection and vm placement in live migration. IEEE Access, 6:7190-7205, 2017. URL: https://doi.org/10.1109/ACCESS.2017.2785280.
  18. Michael Mitzenmacher and Sergei Vassilvitskii. Algorithms with predictions. Communications of the ACM, 65(7):33-35, 2022. URL: https://doi.org/10.1145/3528087.
  19. Saloua El Motaki, Ali Yahyaouy, and Hamid Gualous. A prediction-based model for virtual machine live migration monitoring in a cloud datacenter. Computing, 103(11):2711-2735, 2021. URL: https://doi.org/10.1007/S00607-021-00981-3.
  20. Maciej Pacut, Mahmoud Parham, and Stefan Schmid. Optimal online balanced partitioning. In INFOCOM 2021, 2021. Google Scholar
  21. Cynthia A. Phillips, Cliff Stein, Eric Torng, and Joel Wein. Optimal time-critical scheduling via resource augmentation (extended abstract). In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, STOC '97, pages 140-149, New York, NY, USA, 1997. Association for Computing Machinery. URL: https://doi.org/10.1145/258533.258570.
  22. Rajmohan Rajaraman and Omer Wasim. Improved bounds for online balanced graph re-partitioning. In 30th Annual European Symposium on Algorithms (ESA 2022), 2022. URL: https://doi.org/10.4230/LIPIcs.ESA.2022.83.
  23. Rajmohan Rajaraman and Omer Wasim. Competitive capacitated online recoloring. In 32nd Annual European Symposium on Algorithms (ESA 2024), 2024. URL: https://doi.org/10.4230/LIPIcs.ESA.2024.95.
  24. Dhruv Rohatgi. Near-optimal bounds for online caching with machine learned advice. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1834-1845. SIAM, 2020. URL: https://doi.org/10.1137/1.9781611975994.112.
  25. Tim Roughgarden. Beyond the worst-case analysis of algorithms. Cambridge University Press, 2021. Google Scholar
  26. A. Schrijver. Theory of linear and integer programming. In Wiley-Interscience series in discrete mathematics and optimization, 1999. Google Scholar
  27. Alexander Schrijver. Theory of linear and integer programming. John Wiley & Sons, 1998. Google Scholar
  28. Jaspreet Singh and Navpreet Kaur Walia. A comprehensive review of cloud computing virtual machine consolidation. IEEE Access, 11:106190-106209, 2023. URL: https://doi.org/10.1109/ACCESS.2023.3314613.
  29. Daniel D. Sleator and Robert E. Tarjan. Amortized efficiency of list update and paging rules. Commun. ACM, 28(2):202-208, February 1985. URL: https://doi.org/10.1145/2786.2793.
  30. Mukundan Sridharan, Prasad Calyam, Aishwarya Venkataraman, and Alex Berryman. Defragmentation of resources in virtual desktop clouds for cost-aware utility-optimal allocation. In 2011 Fourth IEEE International Conference on Utility and Cloud Computing, pages 253-260. IEEE, 2011. URL: https://doi.org/10.1109/UCC.2011.41.
  31. Ruitao Xie, Xiaohua Jia, Kan Yang, and Bo Zhang. Energy saving virtual machine allocation in cloud computing. In 2013 IEEE 33rd International Conference on Distributed Computing Systems Workshops, pages 132-137. IEEE, 2013. URL: https://doi.org/10.1109/ICDCSW.2013.37.
  32. Hiroki Yanagisawa, Takayuki Osogami, and Rudy Raymond. Dependable virtual machine allocation. In 2013 Proceedings IEEE INFOCOM, pages 629-637. IEEE, 2013. URL: https://doi.org/10.1109/INFCOM.2013.6566848.
  33. N. Young. The k-server dual and loose competitiveness for paging. Algorithmica, 11(6):525-541, June 1994. URL: https://doi.org/10.1007/BF01189992.
  34. Neal E. Young. On-line file caching. In Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '98, pages 82-86, USA, 1998. Society for Industrial and Applied Mathematics. URL: http://dl.acm.org/citation.cfm?id=314613.314658.
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