A quasi-PTAS for profit-maximizing pricing on line graphs

Authors:
Khaled Elbassioni;René Sitters;Yan Zhang
Affiliations:
Max-Planck-Institut für Informatik, Saarbrücken, Germany;Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands;Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong, China
Venue:
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Year:
2007

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Abstract

We consider the problem of pricing items so as to maximize the profit made from selling these items. An instance is given by a set E of n items and a set of m clients, where each client is specified by one subset of E (the bundle of items he/she wants to buy), and a budget (valuation), which is the maximum price he is willing to pay for that subset. We restrict our attention to the model where the subsets can be arranged such that they form intervals of a line graph. Assuming an unlimited supply of any item, this problem is known as the highway problem and so far only an O(log n)- approximation algorithm is known. We show that a PTAS is likely to exist by presenting a quasi-polynomial time approximation scheme.We also combine our ideas with a recently developed quasi-PTAS for the unsplittable flow problem on line graphs to extend this approximation scheme to the limited supply version of the pricing problem.