Generating and Searching Sets Induced by Networks
Proceedings of the 7th Colloquium on Automata, Languages and Programming
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
Robust subgraphs for trees and paths
ACM Transactions on Algorithms (TALG)
Item pricing for revenue maximization
Proceedings of the 9th ACM conference on Electronic commerce
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
On Hardness of Pricing Items for Single-Minded Bidders
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Combination Can Be Hard: Approximability of the Unique Coverage Problem
SIAM Journal on Computing
On Profit-Maximizing Pricing for the Highway and Tollbooth Problems
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
A quasi-PTAS for profit-maximizing pricing on line graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Pricing commodities, or how to sell when buyers have restricted valuations
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Near-optimal pricing in near-linear time
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Improved orientations of physical networks
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
On the hardness of pricing loss-leaders
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Pricing on paths: a PTAS for the highway problem
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A QPTAS for ε-envy-free profit-maximizing pricing on line graphs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Improved approximation for orienting mixed graphs
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
On the complexity of the highway problem
Theoretical Computer Science
A path-decomposition theorem with applications to pricing and covering on trees
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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An instance of the tollbooth problem consists of an undirected network and a collection of single-minded customers, each of which is interested in purchasing a fixed path subject to an individual budget constraint. The objective is to assign a per-unit price to each edge in a way that maximizes the collective revenue obtained from all customers. The revenue generated by any customer is equal to the overall price of the edges in her desired path, when this cost falls within her budget; otherwise, that customer will not purchase any edge. Our main result is a deterministic algorithm for the tollbooth problem on trees whose approximation ratio is O(log m/log logm), where m denotes the number of edges in the underlying graph. This finding improves on the currently best performance guarantees for trees, due to Elbassioni et al. (SAGT '09), as well as for paths (commonly known as the highway problem), due to Balcan and Blum (EC '06). An additional interesting consequence is a computational separation between tollbooth pricing on trees and the original prototype problem of single-minded unlimited supply pricing, under a plausible hardness hypothesis due to Demaine et al. (SODA '06).