Abstract
The highway pricing problem asks for prices to be determined for segments of a single highway such as to maximize the revenue obtainable from a given set of customers with known valuations. The problem is NP-hard and a recent quasi-PTAS suggests that a PTAS might be in reach. Yet, so far it has resisted any attempt for constant-factor approximation algorithms. We relate the tractability of the problem to structural properties of customers’ valuations. We show that the problem becomes NP-hard as soon as the average valuations of customers are not homogeneous, even under further restrictions such as monotonicity. Moreover, we derive an efficient approximation algorithm, parameterized along the inhomogeneity of customers’ valuations. Finally, we discuss extensions of our results that go beyond the highway pricing problem.
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References
Balcan, M.F., Blum, A.: Approximation Algorithms and Online Mechanisms for Item Pricing. In: Proceedings of the 7th ACM Conference on Electronic Commerce, pp. 29–35. ACM, New York (2006)
Briest, P., Krysta, P.: Single-Minded Unlimited Supply Pricing on Sparse Instances. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1093–1102. ACM-SIAM (2006)
Demaine, E.D., Feige, U., Hajiaghayi, M.T., Salavatipour, M.R.: Combination Can Be Hard: Approximability of the Unique Coverage Problem. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 162–171. ACM-SIAM (2006)
Elbassioni, K., Raman, R., Ray, S., Sitters, R.: On Profit-Maximizing Pricing for the Highway and Tollbooth Problems. Retrieved from arXiv:0901.1140v3 (June 2009)
Elbassioni, K., Sitters, R., Zhang, Y.: A Quasi-PTAS for Profit-Maximizing Pricing on Line Graphs. In: Arge, L., Hoffmann, M., Welzl, E. (eds.) ESA 2007. LNCS, vol. 4698, pp. 451–462. Springer, Heidelberg (2007)
Garey, M.R., Johnson, D.S.: Computers and Intractability: a Quide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)
Grigoriev, A., van Loon, J., Sitters, R., Uetz, M.: Optimal Pricing of Capacitated Networks. Networks 53(1), 79–87 (2009)
Grigoriev, A., van Loon, J., Sviridenko, M., Uetz, M., Vredeveld, T.: Bundle Pricing with Comparable Items. In: Arge, L., Hoffmann, M., Welzl, E. (eds.) ESA 2007. LNCS, vol. 4698, pp. 475–486. Springer, Heidelberg (2007)
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. ACM-SIAM (2005)
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Grigoriev, A., van Loon, J., Uetz, M. (2010). On the Complexity of the Highway Pricing Problem. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_39
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DOI: https://doi.org/10.1007/978-3-642-11266-9_39
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