Abstract
We consider the Max-Buying Problem with Limited Supply, in which there are n items, with C i copies of each item i, and m bidders such that every bidder b has valuation v ib for item i. The goal is to find a pricing p and an allocation of items to bidders that maximize the profit, where every item is allocated to at most C i bidders, every bidder receives at most one item and if a bidder b receives item i then p i ≤ v ib . Briest and Krysta presented a 2-approximation for this problem and Aggarwal et al. presented a 4-approximation for the Price Ladder variant where the pricing must be non-increasing (that is, p 1 ≥ p 2 ≥ ⋯ ≥ p n ). We present a randomized e/(e − 1)-approximation for the Max-Buying Problem with Limited Supply and, for every ε > 0, a (2 + ε)-approximation for the Price Ladder variant.
Research partially supported by CNPq (Proc. 309657/2009-1 and 475064/2010-0) and FAPESP (Proc. 2009/00387-7 and 2013/03447-6).
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References
Aggarwal, G., Feder, T., Motwani, R., Zhu, A.: Algorithms for multi-product pricing. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 72–83. Springer, Heidelberg (2004)
Briest, P.: Uniform budgets and the envy-free pricing problem. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 808–819. Springer, Heidelberg (2008)
Briest, P., Krysta, P.: Buying cheap is expensive: hardness of non-parametric multi-product pricing. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (2007)
Burkard, R.E., Dell’Amico, M., Martello, S.: Assignment problems. SIAM (2009)
Chalermsook, P., Chuzhoy, J., Kannan, S., Khanna, S.: Improved hardness results for profit maximization pricing problems with unlimited supply. In: Gupta, A., Jansen, K., Rolim, J., Servedio, R. (eds.) APPROX 2012 and RANDOM 2012. LNCS, vol. 7408, pp. 73–84. Springer, Heidelberg (2012)
Chalermsook, P., Laekhanukit, B., Nanongkai, D.: Independent set, induced matching, and pricing: Connections and tight (subexponential time) approximation hardnesses. In: 54th Annual IEEE Symposium on Foundations of Computer Science (2013)
Erdös, P., Selfridge, J.: On a combinatorial game. Journal of Combinatorial Theory, Series A 14(3), 298–301 (1973)
Garey, M.R., Johnson, D.S.: Computers and intractibility. W. H. Freeman (1979)
Guruswami, V., Hartline, J.D., Karlin, A.R., Kempe, D., Kenyon, C., McSherry, F.: On profit-maximizing envy-free pricing. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1164–1173 (2005)
Hochbaum, D.: Heuristics for the fixed cost median problem. Mathematical Programming 22(1), 148–162 (1982)
Karmarkar, N., Karp, R.: An efficient approximation scheme for the one-dimensional bin-packing problem. In: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science, pp. 312–320 (1982)
Kuhn, H.W.: The Hungarian Method for the assignment problem. Naval Research Logistics Quarterly 2(1-2), 83–97 (1955)
Oren, S., Smith, S., Wilson, R.: Product line pricing. Journal of Business 57(1), S73–S79 (1984)
Oren, S.S., Smith, S.A., Wilson, R.B.: Multi-product pricing for electric power. Energy Economics 9(2), 104–114 (1987)
Rusmevichientong, P., Roy, B.V., Glynn, P.W.: A nonparametric approach to multiproduct pricing. Operations Research 54(1), 82–98 (2006)
Sen, S.: Issues in optimal product design. In: Analytic Approaches to Product and Marketing Planning: The Second Conference, pp. 265–274 (1982)
Smith, S.A.: New product pricing in quality sensitive markets. Marketing Science 5(1), 70–87 (1986)
Spencer, J.: Ten lectures on the probabilistic method. Society for Industrial and Applied Mathematics (1987)
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Fernandes, C.G., Schouery, R.C.S. (2014). Approximation Algorithms for the Max-Buying Problem with Limited Supply. In: Pardo, A., Viola, A. (eds) LATIN 2014: Theoretical Informatics. LATIN 2014. Lecture Notes in Computer Science, vol 8392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54423-1_61
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DOI: https://doi.org/10.1007/978-3-642-54423-1_61
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