New Online Algorithms for Story Scheduling in Web Advertising

  • Susanne Albers
  • Achim Passen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7966)


We study storyboarding where advertisers wish to present sequences of ads (stories) uninterruptedly on a major ad position of a web page. These jobs/stories arrive online and are triggered by the browsing history of a user who at any time continues surfing with probability β. The goal of an ad server is to construct a schedule maximizing the expected reward. The problem was introduced by Dasgupta, Ghosh, Nazerzadeh and Raghavan (SODA’09) who presented a 7-competitive online algorithm. They also showed that no deterministic online strategy can achieve a competitiveness smaller than 2, for general β.

We present improved algorithms for storyboarding. First we give a simple online strategy that achieves a competitive ratio of 4/(2 − β), which is upper bounded by 4 for any β. The algorithm is also 1/(1 − β)-competitive, which gives better bounds for small β. As the main result of this paper we devise a refined algorithm that attains a competitive ratio of c = 1 + φ, where \(\phi=(1+\sqrt{5})/2\) is the Golden Ratio. This performance guarantee of c ≈ 2.618 is close to the lower bound of 2. Additionally, we study for the first time a problem extension where stories may be presented simultaneously on several ad positions of a web page. For this parallel setting we provide an algorithm whose competitive ratio is upper bounded by \(1/(3-2\sqrt{2})\approx 5.828\), for any β. All our algorithms work in phases and have to make scheduling decisions only every once in a while.


Continue Phase Competitive Ratio Online Algorithm Golden Ratio Online Advertising 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Buchbinder, N., Feldman, M., Ghosh, A., Naor, J(S.): Frequency capping in online advertising. In: Dehne, F., Iacono, J., Sack, J.-R. (eds.) WADS 2011. LNCS, vol. 6844, pp. 147–158. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Buchbinder, N., Jain, K., Naor, J(S.): Online primal-dual algorithms for maximizing ad-auctions revenue. In: Arge, L., Hoffmann, M., Welzl, E. (eds.) ESA 2007. LNCS, vol. 4698, pp. 253–264. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Dasgupta, A., Ghosh, A., Nazerzadeh, H., Raghavan, P.: Online story scheduling in web adverstising. In: Proc. 20th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1275–1284 (2009)Google Scholar
  4. 4.
  5. 5.
    Feldman, J., Korula, N., Mirrokni, V., Muthukrishnan, S., Pál, M.: Online ad assignment with free disposal. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 374–385. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Feige, U., Immorlica, N., Mirrokni, V.S., Nazerzadeh, H.: A combinatorial allocation mechanism with penalties for banner advertising. In: Proc. 17th International Conferene on World Wide Web, pp. 169–178 (2008)Google Scholar
  7. 7.
    Feldman, J., Mehta, A., Mirrokni, V.S., Muthukrishnan, S.: Online stochastic matching: Beating 1-1/e. In: Proc. 50th Annual IEEE Symposium on Foundations of Computer Science, pp. 117–126 (2009)Google Scholar
  8. 8.
    Ghosh, A., Sayedi, A.: Expressive auctions for externalities in online advertising. In: Proc. 19th International Conferene on World Wide Web, pp. 371–380 (2010)Google Scholar
  9. 9.
  10. 10. Surround session,
  11. 11.
    Mehta, A., Saberi, A., Vazirani, U.V., Vazirani, V.V.: AdWords and generalized online matching. Journal of the ACM 54(5) (2007)Google Scholar
  12. 12.
    Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communications of the ACM 28, 202–208 (1985)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Susanne Albers
    • 1
  • Achim Passen
    • 1
  1. 1.Department of Computer ScienceHumboldt-Universität zu BerlinGermany

Personalised recommendations