Online Primal-Dual Algorithms for Maximizing Ad-Auctions Revenue

  • Niv Buchbinder
  • Kamal Jain
  • Joseph (Seffi) Naor
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4698)


We study the online ad-auctions problem introduced by Mehta et al. [15]. We design a (1 − 1/e)-competitive (optimal) algorithm for the problem, which is based on a clean primal-dual approach, matching the competitive factor obtained in [15]. Our basic algorithm along with its analysis are very simple. Our results are based on a unified approach developed earlier for the design of online algorithms [7,8]. In particular, the analysis uses weak duality rather than a tailor made (i.e., problem specific) potential function. We show that this approach is useful for analyzing other classical online algorithms such as ski rental and the TCP-acknowledgement problem. We are confident that the primal-dual method will prove useful in other online scenarios as well.

The primal-dual approach enables us to extend our basic ad-auctions algorithm in a straight forward manner to scenarios in which additional information is available, yielding improved worst case competitive factors. In particular, a scenario in which additional stochastic information is available to the algorithm, a scenario in which the number of interested buyers in each product is bounded by some small number d, and a general risk management framework.


Bipartite Graph Competitive Ratio Allocation Algorithm Online Algorithm Dual Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Alon, N., Awerbuch, B., Azar, Y., Buchbinder, N., Naor, J.: The online set cover problem. In: Proceedings of the 35th STOC, pp. 100–105 (2003)Google Scholar
  2. 2.
    Andelman, N., Mansour, Y.: Auctions with budget constraints. In: Proc. of the 9th Scandinavian Workshop on Algorithm Theory, pp. 26–38 (2004)Google Scholar
  3. 3.
    Aspnes, J., Azar, Y., Fiat, A., Plotkin, S., Waarts, O.: On-line routing of virtual circuits with applications to load balancing and machine scheduling. J. ACM 44(3), 486–504 (1997)zbMATHCrossRefGoogle Scholar
  4. 4.
    Awerbuch, B., Azar, Y., Plotkin, S.: Throughput-competitive online routing. In: Proc. of the 34th Annual Symposium on Foundations of Computer Science, pp. 32–40 (1993)Google Scholar
  5. 5.
    Blum, A., Hartline, J.: Near-optimal online auctions (2005)Google Scholar
  6. 6.
    Borgs, C., Chayes, J., Immorlica, N., Mahdian, M., Saberi, A.: Multi-unit auctions with budget-constrained bidders. In: Proc. of the 6th EC, pp. 44–51 (2005)Google Scholar
  7. 7.
    Buchbinder, N., Naor, J.: Online primal-dual algorithms for covering and packing problems. In: Proc. of the 13th Annual European Symposium on Algorithms, pp. 689–701 (2005)Google Scholar
  8. 8.
    Buchbinder, N., Naor, J.: A primal-dual approach to online routing and packing. In: Proc. of the 47th Annual Symposium on Foundations of Computer Science, pp. 293–204 (2006)Google Scholar
  9. 9.
    Dooly, D.R., Goldman, S., Scott, S.D.: On-line analysis of the TCP acknowledgement delay problem. Journal of the ACM 48, 243–273 (2001)CrossRefGoogle Scholar
  10. 10.
    Goel, A., Meyerson, A., Plotkin, S.A.: Combining fairness with throughput: Online routing with multiple objectives. J. Comput. Syst. Sci. 63(1), 62–79 (2001)zbMATHCrossRefGoogle Scholar
  11. 11.
    Kalyanasundaram, B., Pruhs, K.R.: An optimal deterministic algorithm for online b -matching. Theoretical Computer Science 233(1-2), 319–325 (2000)zbMATHCrossRefGoogle Scholar
  12. 12.
    Karlin, A.R., Kenyon, C., Randall, D.: Dynamic TCP acknowledgement and other stories about e/(e-1). In: Proc. of the 33rd Symposium on Theory of Computing, pp. 502–509 (2001)Google Scholar
  13. 13.
    Karp, R., Vazirani, U., Vazirani, V.: An optimal algorithm for online bipartite matching. In: Proceedings of the 22nd Annual Symposium on Theory of Computing, pp. 352–358 (1990)Google Scholar
  14. 14.
    Mahdian, M., Saberi, A.: Multi-unit auctions with unknown supply. In: EC 2006. Proceedings of the 7th ACM conference on Electronic commerce, pp. 243–249 (2006)Google Scholar
  15. 15.
    Mehta, A., Saberi, A., Vazirani, U., Vazirani, V.: Adwords and generalized on-line matching. In: Proc. of the 46th IEEE Symp. on Foundations of Computer Science, pp. 264–273 (2005)Google Scholar
  16. 16.
    Robinson, S.: Computer scientists optimize innovative ad auction. SIAM News 38, 243–273 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Niv Buchbinder
    • 1
  • Kamal Jain
    • 2
  • Joseph (Seffi) Naor
    • 1
  1. 1.Computer Science Department, Technion, HaifaIsrael
  2. 2.Microsoft Research, Redmond, WA 

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