Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
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
A quasi-PTAS for unsplittable flow on line graphs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximation algorithms and online mechanisms for item pricing
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
A Nonparametric Approach to Multiproduct Pricing
Operations Research
Buying cheap is expensive: hardness of non-parametric multi-product pricing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Uniform Budgets and the Envy-Free Pricing Problem
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
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
A sublogarithmic approximation for highway and tollbooth pricing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
How to sell a graph: guidelines for graph retailers
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Pricing on paths: a PTAS for the highway problem
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On the complexity of the highway problem
Theoretical Computer Science
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We consider the problem of pricing edges of a line graph so as to maximize the profit made from selling intervals to single-minded customers. An instance is given by a set E of n edges with a limited supply for each edge, and a set of m clients, where each client j specifies one interval of E she is interested in and a budget Bj which is the maximum price she is willing to pay for that interval. An envy-free pricing is one in which every customer is allocated (possibly empty) interval maximizing her utility. Recently, Grandoni and Rothvoss (SODA 2011) gave a polynomial-time approximation scheme (PTAS) for the unlimited supply case with running time. By utilizing the known hierarchical decomposition of doubling metrics, we give a PTAS with running time. We then consider the limited supply case, and the notion of -envy-free pricing in which a customer gets an allocation maximizing her utility within an additive error of. For this case we develop an approximation scheme with running time, where $H_e=\frac{B_{\max}(e)}{B_{\min}(e)}$ is the maximum ratio of the budgets of any two customers demanding edge e. This yields a PTAS in the uniform budget case, and a quasi-PTAS for the general case.