A QPTAS for Open image in new window-Envy-Free Profit-Maximizing Pricing on Line Graphs

  • Khaled Elbassioni
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)

Abstract

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 B j 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 Open image in new window . By utilizing the known hierarchical decomposition of doubling metrics, we give a PTAS with running time Open image in new window . We then consider the limited supply case, and the notion of Open image in new window -envy-free pricing in which a customer gets an allocation maximizing her utility within an additive error of Open image in new window . For this case we develop an approximation scheme with running time Open image in new window , 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.

Keywords

Dynamic Programming Line Graph Limited Supply Price Problem Combinatorial Auction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2012

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  • Khaled Elbassioni

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