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

Khaled Elbassioni*, René Sitters, Zhang Yan

*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review

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.

Original languageEnglish
Title of host publicationAlgorithms - ESA 2007 - 15th Annual European Symposium, Proceedings
Pages451-462
Number of pages12
Volume4698 LNCS
Publication statusPublished - 2007
Event15th Annual European Symposium on Algorithms, ESA 2007 - Eilat, Israel
Duration: 8 Oct 200710 Oct 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4698 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Conference

Conference15th Annual European Symposium on Algorithms, ESA 2007
CountryIsrael
CityEilat
Period8/10/0710/10/07

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