Abstract
Chunked-reward advertising is commonly used in the industry, such as the guaranteed delivery in display advertising and the daily-deal services (e.g., Groupon) in online shopping. In chunked-reward advertising, the publisher promises to deliver at least a certain volume (a.k.a. tipping point or lower bound) of user traffic to an advertiser according to their mutual contract. At the same time, the advertiser may specify a maximum volume (upper bound) of traffic that he/she would like to pay for according to his/her budget constraint. The objective of the publisher is to design an appropriate mechanism to allocate the user traffic so as to maximize the overall revenue obtained from all such advertisers. In this paper, we perform a formal study on this problem, which we call Chunked-reward Allocation Problem (CAP). In particular, we formulate CAP as a knapsack-like problem with variable-sized items and majorization constraints. Our main results regarding CAP are as follows. (1) We first show that for a special case of CAP, in which the lower bound equals the upper bound for each contract, there is a simple dynamic programming-based algorithm that can find an optimal allocation in pseudo-polynomial time. (2) The general case of CAP is much more difficult than the special case. To solve the problem, we first discover several structural properties of the optimal allocation, and then design a two-layer dynamic programming-based algorithm that can find an optimal allocation in pseudo-polynomial time by leveraging these properties. (3) We convert the two-layer dynamic programming based algorithm to a fully polynomial time approximation scheme (FPTAS). Besides these results, we also investigate some natural generalizations of CAP, and propose effective algorithms to solve them.
This work was conducted at Microsoft Research Asia.
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References
Aggarwal, G., Goel, A., Motwani, R.: Truthful auctions for pricing search keywords. In: Proceedings of the 7th ACM Conference on Electronic Commerce, pp. 1–7. ACM (2006)
Brucker, P.: Scheduling algorithms, 5th edn., pp. 124–125. Springer (2007)
Ebenlendr, T., Sgall, J.: Optimal and online preemptive scheduling on uniformly related machines. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 199–210. Springer, Heidelberg (2004)
Edelman, B., Ostrovsky, M., Schwarz, M.: Internet advertising and the generalized second price auction: Selling billions of dollars worth of keywords. Technical report, National Bureau of Economic Research (2005)
Epstein, L., Jez, L., Sgall, J., van Stee, R.: Online interval scheduling on uniformly related machines (2012) (manuscript)
Goel, A., Meyerson, A.: Simultaneous optimization via approximate majorization for concave profits or convex costs. Algorithmica 44(4), 301–323 (2006)
Horvath, E.C., Lam, S., Sethi, R.: A level algorithm for preemptive scheduling. Journal of the ACM (JACM) 24(1), 32–43 (1977)
Ibarra, O.H., Kim, C.E.: Fast approximation algorithms for the knapsack and sum of subset problems. Journal of the ACM (JACM) 22(4), 463–468 (1975)
Kong, W., Li, J., Qin, T., Liu, T.-Y.: Optimal allocation for chunked-reward advertising. arXiv preprint arXiv:1305.5946 (2013)
Lipton, R.: Online interval scheduling. In: Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 302–311. Society for Industrial and Applied Mathematics (1994)
Nielsen, M.A.: An introduction to majorization and its applications to quantum mechanics (2002)
Pinedo, M.: Scheduling: theory, algorithms, and systems. Springer (2008)
Vazirani, V.V.: Approximation algorithms. Springer (2004)
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Kong, W., Li, J., Liu, TY., Qin, T. (2013). Optimal Allocation for Chunked-Reward Advertising. In: Chen, Y., Immorlica, N. (eds) Web and Internet Economics. WINE 2013. Lecture Notes in Computer Science, vol 8289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45046-4_24
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DOI: https://doi.org/10.1007/978-3-642-45046-4_24
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