Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On profit-maximizing envy-free pricing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Combination can be hard: approximability of the unique coverage problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Single-minded unlimited supply pricing on sparse instances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation algorithms and online mechanisms for item pricing
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
A quasi-PTAS for profit-maximizing pricing on line graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Bundle pricing with comparable items
ESA'07 Proceedings of the 15th annual European conference on Algorithms
On the hardness of pricing loss-leaders
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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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.