Abstract
We study the following TV ad placement problem: m identical time-slots are on sell within a period of m days and only one time-slot is available each day. Advertisers arrive online to bid for some time-slots to publish their ads. Typically, advertiser i arrives at the a i ’th day and wishes that her ad would be published for at most s i days. The ad cannot be published after its expiration time, the d i ’th day. If the ad is published for x i ≤ s i days, the total value of the ad for advertiser i is x i ·v i ; otherwise, the value of the ad to be published for each day diminishes and the total value is always s i ·v i . Our goal is to maximize the social welfare: the sum of values of the published ads. As usual in many online mechanisms, we are aiming to optimize the competitive ratio: the worst ratio between the optimal social welfare and the social welfare achieved by our mechanism.
Our main result is a competitive online mechanism which is truthful and prompt for the TV ad placement problem. In the mechanism, each advertiser is motivated to report her private value v i truthfully and can learn her payment at the very moment that she wins some time-slots. Before studying the general case where the maximum demands s i ’s are non-uniform, we study the special case where all s i ’s are uniform and prove that our mechanism achieves a non-trivial competitive ratio of 5. For the general case where the maximum demands s i ’s are non-uniform, we prove that our mechanism achieves a competitive ratio of 5·⌈s max /s min ⌉, where s max , s min are the maximum and minimum value of s i ’s. Besides, we derive a lower bound of \(\min\{\frac{v_{max} + v_{min}}{2 v_{min}}, \frac{s_{max}}{s_{min}}\}\) on the competitive ratio for the general case, where v max , v min are the maximum and minimum value of v i ’s.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aggarwal, G., Goel, G., Karande, C., Mehta, A.: Online vertex-weighted bipartite matching and single-bid budgeted allocations. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1253–1264. SIAM (2011)
Aggarwal, G., Hartline, J.D.: Knapsack auctions. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, pp. 1083–1092. ACM (2006)
Archer, A., Tardos, É.: Truthful mechanisms for one-parameter agents. In: Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science, pp. 482–491. IEEE (2001)
Azar, Y., Khaitsin, E.: Prompt mechanism for ad placement over time. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 19–30. Springer, Heidelberg (2011)
Bartal, Y., Chin, F.Y.L., Chrobak, M., Fung, S.P.Y., Jawor, W., Lavi, R., Sgall, J., Tichý, T.: Online competitive algorithms for maximizing weighted throughput of unit jobs. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 187–198. Springer, Heidelberg (2004)
Borgs, C., Chayes, J., Etesami, O., Immorlica, N., Jain, K., Mahdian, M.: Dynamics of bid optimization in online advertisement auctions. In: Proceedings of the 16th International Conference on World Wide Web, pp. 531–540. ACM (2007)
Chan, W.-T., Lam, T.-W., Ting, H.-F., Wong, P.W.H.: New results on on-demand broadcasting with deadline via job scheduling with cancellation. In: Chwa, K.-Y., Munro, J.I. (eds.) COCOON 2004. LNCS, vol. 3106, pp. 210–218. Springer, Heidelberg (2004)
Chin, F.Y.L., Fung, S.P.Y.: Online scheduling with partial job values: Does timesharing or randomization help? Algorithmica 37(3), 149–164 (2003)
Chrobak, M., Jawor, W., Sgall, J., Tichý, T.: Improved online algorithms for buffer management in qoS switches. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 204–215. Springer, Heidelberg (2004)
Cole, R., Dobzinski, S., Fleischer, L.K.: Prompt mechanisms for online auctions. In: Monien, B., Schroeder, U.-P. (eds.) SAGT 2008. LNCS, vol. 4997, pp. 170–181. Springer, Heidelberg (2008)
Englert, M., Westermann, M.: Considering suppressed packets improves buffer management in qos switches. In: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 209–218. Society for Industrial and Applied Mathematics (2007)
Nisan, N., Bayer, J., Chandra, D., Franji, T., Gardner, R., Matias, Y., Rhodes, N., Seltzer, M., Tom, D., Varian, H., Zigmond, D.: Google’s auction for tv ads. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part II. LNCS, vol. 5556, pp. 309–327. Springer, Heidelberg (2009)
Ting, H.-F.: A near optimal scheduler for on-demand data broadcasts. In: Calamoneri, T., Finocchi, I., Italiano, G.F. (eds.) CIAC 2006. LNCS, vol. 3998, pp. 163–174. Springer, Heidelberg (2006)
Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. The Journal of Finance 16(1), 8–37 (1961)
Zhou, Y., Chakrabarty, D., Lukose, R.: Budget constrained bidding in keyword auctions and online knapsack problems. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 566–576. Springer, Heidelberg (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Xiang, X. (2013). Prompt Mechanism for Online Auctions with Multi-unit Demands. In: Widmayer, P., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2013. Lecture Notes in Computer Science, vol 8287. Springer, Cham. https://doi.org/10.1007/978-3-319-03780-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-03780-6_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03779-0
Online ISBN: 978-3-319-03780-6
eBook Packages: Computer ScienceComputer Science (R0)