Online Balanced Repartitioning

  • Chen Avin
  • Andreas Loukas
  • Maciej Pacut
  • Stefan SchmidEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9888)


Distributed cloud applications, including batch processing, streaming, and scale-out databases, generate a significant amount of network traffic and a considerable fraction of their runtime is due to network activity. This paper initiates the study of deterministic algorithms for collocating frequently communicating nodes in a distributed networked systems in an online fashion. In particular, we introduce the Balanced RePartitioning (BRP) problem: Given an arbitrary sequence of pairwise communication requests between n nodes, with patterns that may change over time, the objective is to dynamically partition the nodes into \(\ell \) clusters, each of size k, at a minimum cost. Every communication request needs to be served: if the communicating nodes are located in the same cluster, the request is served locally, at cost 0; if the nodes are located in different clusters, the request is served remotely using inter-cluster communication, at cost 1. The partitioning can be updated dynamically (i.e., repartitioned), by migrating nodes between clusters at cost \(\alpha \) per node migration. The goal is to devise online algorithms which find a good trade-off between the communication and the migration cost, i.e., “rent” or “buy”, while maintaining partitions which minimize the number of inter-cluster communications. BRP features interesting connections to other well-known online problems. In particular, we show that scenarios with \(\ell =2\) generalize online paging, and scenarios with \(k=2\) constitute a novel online version of maximum matching. We consider settings both with and without cluster-size augmentation. Somewhat surprisingly (and unlike online paging), we prove that any deterministic online algorithm has a competitive ratio of at least k, even with augmentation. Our main technical contribution is an \(O(k \log {k})\)-competitive deterministic algorithm for the setting with (constant) augmentation. This is attractive as, in contrast to \(\ell \), k is likely to be small in practice. For the case of matching (\(k=2\)), we present a constant competitive algorithm that does not rely on augmentation.


Dynamic graphs Clustering Graph partitioning Algorithms Competitive analysis Cloud computing 


  1. 1.
    Adamaszek, A., Czumaj, A., Englert, M., Räcke, H.: An O(log k)-competitive algorithm for generalized caching. In: Proceedings of 23rd SODA, pp. 1681–1689 (2012)Google Scholar
  2. 2.
    Al-Fares, M., Loukissas, A., Vahdat, A.: A scalable, commodity data center network architecture. ACM SIGCOMM CCR 38(4), 63–74 (2008)CrossRefGoogle Scholar
  3. 3.
    Andreev, K., Räcke, H.: Balanced graph partitioning. In: Proceedings of 16th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) (2004)Google Scholar
  4. 4.
    Andreev, K., Räcke, H.: Balanced graph partitioning. Theory Comput. Syst. 39(6), 929–939 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Arora, S., Rao, S., Vazirani, U.: Expander flows, geometric embeddings and graph partitioning. J. ACM (JACM) 56(2), 5 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Avin, C., Loukas, A., Pacut, M., Schmid, S.: Online balanced repartitioning. arXiv (2016)
  7. 7.
    Awerbuch, B., Bartal, Y., Fiat, A.: Competitive distributed file allocation. Inf. Comput. 185(1), 1–40 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Mach. Learn. 56(1–3), 89–113 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Bartal, Y., Charikar, M., Indyk, P.: On page migration and other relaxed task systems. Theor. Comput. Sci. 268(1), 43–66 (2001). Also appeared in Proceedings of the 8th SODA, pp. 43–52 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Bienkowski, M., Feldmann, A., Grassler, J., Schaffrath, G., Schmid, S.: The wide-area virtual service migration problem: a competitive analysis approach. IEEE/ACM Trans. Netw. 22(1), 165–178 (2014)CrossRefGoogle Scholar
  11. 11.
    Borodin, A., Linial, N., Saks, M.E.: An optimal on-line algorithm for metrical task system. J. ACM 39(4), 745–763 (1992). Also appeared in Proceedings of the 19th STOC, pp. 373–382 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Brehob, M., Enbody, R.J., Torng, E., Wagner, S.: On-line restricted caching. J. Sched. 6(2), 149–166 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Buchbinder, N., Chen, S., Naor, J.S.: Competitive algorithms for restricted caching and matroid caching. In: Schulz, A.S., Wagner, D. (eds.) ESA 2014. LNCS, vol. 8737, pp. 209–221. Springer, Heidelberg (2014)Google Scholar
  14. 14.
    Chowdhury, M., Zaharia, M., Ma, J., Jordan, M.I., Stoica, I.: Managing data transfers in computer clusters with orchestra. SIGCOMM CCR 41(4), 98–109 (2011)CrossRefGoogle Scholar
  15. 15.
    Ding, C.H.Q., He, X., Zha, H., Gu, M., Simon, H.D.: A min-max cut algorithm for graph partitioning and data clustering. In: Proceedings of IEEE International Conference on Data Mining (ICDM), pp. 107–114 (2001)Google Scholar
  16. 16.
    Epstein, L., Imreh, C., Levin, A., Nagy-György, J.: Online file caching with rejection penalties. Algorithmica 71(2), 279–306 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Feige, U., Krauthgamer, R.: A polylogarithmic approximation of the minimum bisection. SIAM J. Comput. 31(4), 1090–1118 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Fiat, A., Karp, R.M., Luby, M., McGeoch, L.A., Sleator, D.D., Young, N.E.: Competitive paging algorithms. J. Algorithms 12(4), 685–699 (1991)CrossRefzbMATHGoogle Scholar
  19. 19.
    Fiat, A., Rabani, Y., Ravid, Y.: Competitive k-server algorithms. J. Comput. Syst. Sci. 48(3), 410–428 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Krauthgamer, R., Feige, U.: A polylogarithmic approximation of the minimum bisection. SIAM Rev. 48(1), 99–130 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Kumar, A., Gupta, A., Roughgarden, T.: A constant-factor approximation algorithm for the multicommodity rent-or-buy problem. In Proceedings of 43rd Symposium on Foundations of Computer Science (FOCS) (2002)Google Scholar
  22. 22.
    Lotker, Z., Patt-Shamir, B., Rawitz, D.: Rent, lease or buy: randomized algorithms for multislope ski rental. In: Proceedings of the 25th Symposium on Theoretical Aspects of Computer Science (STACS), pp. 503–514 (2008)Google Scholar
  23. 23.
    McGeoch, L.A., Sleator, D.D.: A strongly competitive randomized paging algorithm. Algorithmica 6(6), 816–825 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Mendel, M., Seiden, S.S.: Online companion caching. Theor. Comput. Sci. 324(2–3), 183–200 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Mogul, J.C., Popa, L.: What we talk about when we talk about cloud network performance. ACM SIGCOMM CCR 42, 44–48 (2012)CrossRefGoogle Scholar
  26. 26.
    Ramanan, P.V., Brown, D.J., Lee, C.C., Lee, D.T.: On-line bin packing in linear time. J. Algorithms 10(3), 305–326 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Schaeffer, S.E.: Graph clustering. Comput. Sci. Rev. 1(1), 27–64 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Seiden, S.S.: On the online bin packing problem. J. ACM 49(5), 640–671 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Young, N.E.: On-line caching as cache size varies. In: Proceedings of the 2nd ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 241–250 (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Chen Avin
    • 1
  • Andreas Loukas
    • 2
  • Maciej Pacut
    • 3
  • Stefan Schmid
    • 2
    • 4
    Email author
  1. 1.Ben Gurion University of the NegevBeershebaIsrael
  2. 2.TU BerlinBerlinGermany
  3. 3.University of WroclawWroclawPoland
  4. 4.Aalborg UniversityAalborgDenmark

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