The Online Set Aggregation Problem

  • Rodrigo A. Carrasco
  • Kirk Pruhs
  • Cliff Stein
  • José Verschae
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10807)


We introduce the online Set Aggregation Problem, which is a natural generalization of the Multi-Level Aggregation Problem, which in turn generalizes the TCP Acknowledgment Problem and the Joint Replenishment Problem. We give a deterministic online algorithm, and show that its competitive ratio is logarithmic in the number of requests. We also give a matching lower bound on the competitive ratio of any randomized online algorithm.


Online algorithms Competitive analysis Set aggregation Multilevel aggregation 


  1. 1.
    Bienkowski, M., Böhm, M., Byrka, J., Chrobak, M., Dürr, C., Folwarcznỳ, L., Jez, L., Sgall, J., Thang, N.K., Veselỳ, P.: Online algorithms for multi-level aggregation. In: European Symposium on Algorithms, pp. 12:1–12:17 (2016)Google Scholar
  2. 2.
    Buchbinder, N., Feldman, M., Naor, J.S., Talmon, O.: O(depth)-competitive algorithm for online multi-level aggregation. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 1235–1244 (2017)Google Scholar
  3. 3.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, New York (1998)zbMATHGoogle Scholar
  4. 4.
    Kalyanasundaram, B., Pruhs, K.: Online weighted matching. J. Algorithms 14(3), 478–488 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Khuller, S., Mitchell, S.G., Vazirani, V.V.: On-line algorithms for weighted bipartite matching and stable marriages. Theor. Comput. Sci. 127(2), 255–267 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Bienkowski, M., Böhm, M., Byrka, J., Chrobak, M., Dürr, C., Folwarcznỳ, L., Jeż, L., Sgall, J., Thang, N.K., Veselỳ, P.: Online algorithms for multi-level aggregation. arXiv preprint arXiv:1507.02378 (2015)
  7. 7.
    Aggarwal, A., Park, J.K.: Improved algorithms for economic lot sizing problems. Oper. Res. 41, 549–571 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Dooly, D.R., Goldman, S.A., Scott, S.D.: On-line analysis of the TCP acknowledgment delay problem. J. ACM 48(2), 243–273 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Karlin, A.R., Kenyon, C., Randall, D.: Dynamic TCP acknowledgement and other stories about e/(e\(\,-\,\)1). Algorithmica 36(3), 209–224 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Bienkowski, M., Byrka, J., Chrobak, M., Jeż, Ł., Nogneng, D., Sgall, J.: Better approximation bounds for the joint replenishment problem. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 42–54 (2014)Google Scholar
  11. 11.
    Buchbinder, N., Kimbrel, T., Levi, R., Makarychev, K., Sviridenko, M.: Online make-to-order joint replenishment model: primal-dual competitive algorithms. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 952–961 (2008)Google Scholar
  12. 12.
    Bienkowski, M., Byrka, J., Chrobak, M., Dobbs, N., Nowicki, T., Sviridenko, M., Świrszcz, G., Young, N.E.: Approximation algorithms for the joint replenishment problem with deadlines. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013. LNCS, vol. 7965, pp. 135–147. Springer, Heidelberg (2013). CrossRefGoogle Scholar
  13. 13.
    Badrinath, B., Sudame, P.: Gathercast: the design and implementation of a programmable aggregation mechanism for the internet. In: International Conference on Computer Communications and Networks, pp. 206–213 (2000)Google Scholar
  14. 14.
    Bortnikov, E., Cohen, R.: Schemes for scheduling of control messages by hierarchical protocols. In: Joint Conference of the IEEE Computer and Communications Societies, vol. 2, pp. 865–872 (1998)Google Scholar
  15. 15.
    Hu, F., Cao, X., May, C.: Optimized scheduling for data aggregation in wireless sensor networks. In: International Conference on Information Technology: Coding and Computing (ITCC 2005), vol. 2, pp. 557–561 (2005)Google Scholar
  16. 16.
    Yuan, W., Krishnamurthy, S., Tripathi, S.: Synchronization of multiple levels of data fusion in wireless sensor networks. In: Global Telecommunications Conference, vol. 1, pp. 221–225 (2003)Google Scholar
  17. 17.
    Papadimitriou, C.H.: Computational aspects of organization theory. In: Diaz, J., Serna, M. (eds.) ESA 1996. LNCS, vol. 1136, pp. 559–564. Springer, Heidelberg (1996). CrossRefGoogle Scholar
  18. 18.
    Crowston, W.B., Wagner, M.H.: Dynamic lot size models for multi-stage assembly systems. Manag. Sci. 20(1), 14–21 (1973)CrossRefzbMATHGoogle Scholar
  19. 19.
    Kimms, A.: Multi-level lot sizing and scheduling: methods for capacitated, dynamic, and deterministic models. Springer, Heidelberg (1997). CrossRefzbMATHGoogle Scholar
  20. 20.
    Lambert, D.M., Cooper, M.C.: Issues in supply chain management. Ind. Mark. Manag. 29(1), 65–83 (2000)CrossRefGoogle Scholar
  21. 21.
    Becchetti, L., Marchetti-Spaccamela, A., Vitaletti, A., Korteweg, P., Skutella, M., Stougie, L.: Latency-constrained aggregation in sensor networks. ACM Trans. Algorithms 6(1), 13:1–13:20 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Pedrosa, L.L.C.: Private communication (2013)Google Scholar
  23. 23.
    Levi, R., Roundy, R., Shmoys, D.B.: Primal-dual algorithms for deterministic inventory problems. Mathematics of Operations Research 31(2), 267–284 (2006)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Facultad de Ingeniería y CienciasUniversidad Adolfo IbáñezSantiagoChile
  2. 2.Department of Computer ScienceUniversity of PittsburghPittsburghUSA
  3. 3.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA
  4. 4.Facultad de Matemáticas & Escuela de IngenieríaPontificia Universidad Católica de ChileSantiagoChile

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