Frontiers of Computer Science

, Volume 13, Issue 2, pp 333–342 | Cite as

Optimal bundles for sponsored search auctions via bracketing scheme

  • Zheng-Dong Xia
  • Tian-Ming BuEmail author
  • Wen-Hui Gong
Research Article


Sponsored search auction has been recently studied and auctioneer’s revenue is an important consideration in probabilistic single-item second-price auctions. Some papers have analyzed the revenue maximization problem on different methods to bundle contexts. In this paper, we propose a more flexible and natural method which is called the bracketing method.We prove that finding a bracketing scheme that maximizes the auctioneer’s revenue is strongly NP-hard. Then, a heuristic algorithm is given. Experiments on three test cases show that the revenue of the optimal bracketing scheme is very close to the optimal revenue without any bundling constraint, and the heuristic algorithm performs very well. Finally, we consider a simpler model that for each row in the valuation matrix, the non-zero cells have the same value. We prove that the revenue maximization problem with K-anonymous signaling scheme and cardinality constrained signaling scheme in this simpler model are both NP-hard.


sponsored search auction revenue maximization bracketing scheme NP-hardness 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



We would like to thank the anonymous reviewers for their many insightful comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 61672012).

Supplementary material

11704_2017_6102_MOESM1_ESM.ppt (112 kb)
Supplementary material, approximately 112 KB.


  1. 1.
    Interactive Advertising Bureau. Iab Internet advertising revenue report 2013 full year results. Technical Report, 2014Google Scholar
  2. 2.
    Fain D C, Pedersen J O. Sponsored search: a brief history. Bulletin of the American Society for Information Science and Technology, 2006, 32(2): 12–13CrossRefGoogle Scholar
  3. 3.
    Jansen B J, Mullen T. Sponsored search: an overview of the concept, history, and technology. International Journal of Electronic Business, 2008, 6(2): 114–131CrossRefGoogle Scholar
  4. 4.
    Qin T, Chen W, Liu T Y. Sponsored search auctions: recent advances and future directions. ACM Transactions on Intelligent Systems and Technology, 2015, 5(4): 60CrossRefGoogle Scholar
  5. 5.
    Even-Dar E, Kearns M, Wortman J. Sponsored search with contexts. In: Proceedings of the 3rd International Workshop on Internet and Network Economics. 2007, 312–317CrossRefGoogle Scholar
  6. 6.
    Ghosh A, Nazerzadeh H, Sundararajan M. Computing optimal bundles for sponsored search. In: Proceedings of the 3rd International Workshop on Internet and Network Economics. 2007, 576–583CrossRefGoogle Scholar
  7. 7.
    Emek Y, Feldman M, Gamzu I, Tennenholtz M. Revenue maximization in probabilistic single-item auctions via signaling. In: Proceedings of the 7th Ad Auctions Workshop. 2011Google Scholar
  8. 8.
    Miltersen B, Sheffet O. Send mixed signals: earn more, work less. In: Proceedings of the 13th ACM Conference on Electronic Commerce. 2012, 234–247Google Scholar
  9. 9.
    Dughmi S, Immorlica N, Roth A. Constrained signaling for welfare and revenue maximization. ACM SIGecom Exchanges, 2013, 12(1): 53–56CrossRefGoogle Scholar
  10. 10.
    Dughmi S, Immorlica N, Roth A. Constrained signaling in auction design. In: Proceedings of the 25th ACM-SIAM Symposium on Discrete Algorithms. 2014, 1341–1357CrossRefGoogle Scholar
  11. 11.
    Dughmi S. On the hardness of signaling. 2014, arXiv preprint arXiv:1402.4194CrossRefGoogle Scholar
  12. 12.
    Chen C, Qin T. k-anonymous signaling scheme. 2013, arXiv preprint arXiv:1311.6638Google Scholar
  13. 13.
    Guo M Y, Deligkas A. Revenue maximization via hiding item attributes. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence. 2013Google Scholar
  14. 14.
    Papadimitriou P, Garcia-Molina H, Dasdan A, Kolay S. Output url bidding. In: Proceedings of the 37th International Conference on Very Large Data Bases. 2010, 161–172Google Scholar
  15. 15.
    Dasdan A, Santanu K, Papadimitriou P, Garcia-Molina H. Output bidding: a new search advertising model complementary to keyword bidding. In: Proceedings of the 5th Workshop on Ad Auctions. 2009Google Scholar
  16. 16.
    Garey M R, Johnson D S. Computers and Intractability: A Guide to the Theory of NP-Completeness. San Francisco: Freeman. 1979zbMATHGoogle Scholar
  17. 17.
    Leyton-Brown K, Pearson M, Shoham Y. Towards a universal test suite for combinatorial auction algorithms. In: Proceedings of the 2nd ACM Conference on Electronic Commerce. 2000, 66–76CrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Shanghai Key Laboratory of Trustworthy ComputingEast China Normal UniversityShanghaiChina

Personalised recommendations