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
Mechanism Design via Machine Learning
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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
How to sell a graph: guidelines for graph retailers
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Near-optimal pricing in near-linear time
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Algorithms for Optimal Price Regulations
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
On the Complexity of the Highway Pricing Problem
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Optimal bundle pricing with monotonicity constraint
Operations Research Letters
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We consider a revenue maximization problem where we are selling a set of items, each available in a certain quantity, to a set of bidders. Each bidder is interested in one or several bundles of items. We assume the bidders' valuations for each of these bundles to be known. Whenever bundle prices are determined by the sum of single item prices, this algorithmic problem was recently shown to be inapproximable to within a semi-logarithmic factor. We consider two scenarios for determining bundle prices that allow to break this inapproximability barrier. Both scenarios are motivated by problems where items are different, yet comparable. First, we consider classical single item prices with an additional monotonicity constraint, enforcing that larger bundles are at least as expensive as smaller ones. We show that the problem remains strongly NP-hard, and we derive a PTAS. Second, motivated by real-life cases, we introduce the notion of affine price functions, and derive fixed-parameter polynomial time algorithms.