Competitive auctions and digital goods
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Competitive Auctions for Multiple Digital Goods
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
On profit-maximizing envy-free pricing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
Optimal envy-free pricing with metric substitutability
Proceedings of the 9th ACM conference on Electronic commerce
Uniform Budgets and the Envy-Free Pricing Problem
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Non-monotone submodular maximization under matroid and knapsack constraints
Proceedings of the forty-first annual ACM symposium on Theory of computing
Near-optimal pricing in near-linear time
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Competitive algorithms for online pricing
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Online pricing for multi-type of items
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Online pricing for bundles of multiple items
Journal of Global Optimization
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The envy-free pricing problem can be stated as finding a pricing and allocation scheme in which each consumer is allocated a set of items that maximize her utility under the pricing. The goal is to maximize seller revenue.We study the problem with general supply constraints which are given as an independence system1 defined over the items. The constraints, for example, can be a number of linear constraints or matroids. This captures the situation where items do not pre-exist, but are produced in reflection of consumer valuation of the items under the limit of resources. This paper focuses on the case of unit-demand consumers. In the setting, there are n consumers and m items; each item may be produced in multiple copies. Each consumer i ∈ [n] has a valuation vij on item j in the set Si in which she is interested. She must be allocated (if any) an item which gives the maximum (non-negative) utility. Suppose we are given an a-approximation oracle for finding the maximum weight independent set for the given independence system (or a slightly stronger oracle); for a large number of natural and interesting supply constraints, constant approximations are available. We obtain the following results. - O(α log n)-approximation for the general case. - O(αk)-approximation when each consumer is interested in at most k distinct types of items. - O(αf)-approximation when each item is interesting to at most f consumers. Note that the final two results were previously unknown even without the independence system constraint.