, Volume 65, Issue 1, pp 60–94 | Cite as

Collecting Weighted Items from a Dynamic Queue

  • Marcin Bienkowski
  • Marek Chrobak
  • Christoph Dürr
  • Mathilde Hurand
  • Artur Jeż
  • Łukasz Jeż
  • Grzegorz Stachowiak
Open Access


We consider online competitive algorithms for the problem of collecting weighted items from a dynamic queue S. The content of S varies over time. An update to S can occur between any two consecutive time steps, and it consists in deleting any number of items at the front of S and inserting other items into arbitrary locations in S. At each time step we are allowed to collect one item in S. The objective is to maximize the total weight of collected items. This is a generalization of bounded-delay packet scheduling (also known as buffer management). We present several upper and lower bounds on the competitive ratio for the general case and for some restricted variants of this problem.


Online algorithms Competitive analysis Packet scheduling Buffer management 


  1. 1.
    Andelman, N., Mansour, Y., Zhu, A.: Competitive queueing policies in QoS switches. In: Proceedings of the 14th Symposium on Discrete Algorithms (SODA), pp. 761–770. ACM/SIAM, New York (2003) Google Scholar
  2. 2.
    Birnbaum, B., Mathieu, C.: On-line bipartite matching made simple. SIGACT News 39(1), 80–87 (2008) CrossRefGoogle Scholar
  3. 3.
    Chin, F.Y.L., Chrobak, M., Fung, S.P.Y., Jawor, W., Sgall, J., Tichý, T.: Online competitive algorithms for maximizing weighted throughput of unit jobs. J. Discrete Algorithms 4, 255–276 (2006) MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Chin, F.Y.L., Fung, S.P.Y.: Online scheduling for partial job values: Does timesharing or randomization help? Algorithmica 37, 149–164 (2003) MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Englert, M., Westermann, M.: Considering suppressed packets improves buffer management in QoS switches. In: Proceedings of the 18th Symposium on Discrete Algorithms (SODA), pp. 209–218. ACM/SIAM, New York (2007) Google Scholar
  6. 6.
    Hajek, B.: On the competitiveness of online scheduling of unit-length packets with hard deadlines in slotted time. In: Conference on Information Sciences and Systems, pp. 434–438 (2001) Google Scholar
  7. 7.
    Jeż, Ł.: One to rule them all: A general randomized algorithm for buffer management with bounded delay. In: Proceedings of the 19th Annual European Symposium on Algorithms (ESA), pp. 239–250 (2011) Google Scholar
  8. 8.
    Kalyanasundaram, B., Pruhs, K.: An optimal deterministic algorithm for online b-matching. Theor. Comput. Sci. 233(1–2), 319–325 (2000) MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Kesselman, A., Lotker, Z., Mansour, Y., Patt-Shamir, B., Schieber, B., Sviridenko, M.: Buffer overflow management in QoS switches. SIAM J. Comput. 33, 563–583 (2004) MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Kesselman, A., Mansour, Y., van Stee, R.: Improved competitive guarantees for QoS buffering. Algorithmica 43, 63–80 (2005) MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Li, F., Sethuraman, J., Stein, C.: An optimal online algorithm for packet scheduling with agreeable deadlines. In: Proceedings of the 16th Symposium on Discrete Algorithms (SODA), pp. 801–802. ACM/SIAM, New York (2005) Google Scholar
  12. 12.
    Li, F., Sethuraman, J., Stein, C.: Better online buffer management. In: Proceedings of the 18th Symposium on Discrete Algorithms (SODA), pp. 199–208. ACM/SIAM, New York (2007) Google Scholar
  13. 13.
    Mehta, A., Saberi, A., Vazirani, U.V., Vazirani, V.V.: Adwords and generalized online matching. J. ACM 54(5), 22 (2007) MathSciNetGoogle Scholar
  14. 14.
    Meteor burst communications.
  15. 15.

Copyright information

© The Author(s) 2011

Authors and Affiliations

  • Marcin Bienkowski
    • 1
  • Marek Chrobak
    • 2
  • Christoph Dürr
    • 3
  • Mathilde Hurand
    • 4
  • Artur Jeż
    • 1
  • Łukasz Jeż
    • 1
  • Grzegorz Stachowiak
    • 1
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland
  2. 2.Department of Computer ScienceUniversity of CaliforniaRiversideUSA
  3. 3.CNRS, LIP6Université Pierre et Marie CurieParis Cedex 05France
  4. 4.GoogleZürichSwitzerland

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